Klienditugi: 7440010 (E-R 10-18)

Survey Sampling Theory and Applications [Pehme köide]

Raghunath Arnab (Department of Statistics, University of Botswana, Botswana, and University of Kwa-Zulu Natal, South Africa)

Formaat: Paperback / softback, 930 pages, kõrgus x laius: 229x152 mm, kaal: 1340 g
Ilmumisaeg: 09-Mar-2017
Kirjastus: Academic Press Inc
ISBN-10: 0128118482
ISBN-13: 9780128118481

Teised raamatud teemal:

Stochastics

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Formaat: Paperback / softback, 930 pages, kõrgus x laius: 229x152 mm, kaal: 1340 g
Ilmumisaeg: 09-Mar-2017
Kirjastus: Academic Press Inc
ISBN-10: 0128118482
ISBN-13: 9780128118481

Teised raamatud teemal:

Stochastics

Püsilink: https://www.kriso.ee/db/9780128118481.html

Märksõnad:

This book provides comprehensive materials on survey sampling offering learners and researchers grounded basics and progressive issues in advanced essentials of sampling theory and practice while advanced students and colleagues in the field will find research-based reflections/ examples on emerging trends from the very beginning to the advanced level. Hence it will be useful for basic and advanced courses of Survey sampling. Some of the books are available for graduate students but do not contain material for the recent developments in the area of survey sampling.

The book covers a wide spectrum of topics on the subject and some of the topics e.g. Repetitive sampling over two occasions with varying probabilities, Ranked set sampling, Fays method for Balanced repeated replications, Mirror-Match bootstrap and Controlled sampling procedures discussed here are not available in other text books. In addition, some of the materials are discussed at an advanced level.

In each section, theories are illustrated with numerical examples. At the end of each chapter theoretical as well as numerical exercises are given which can help graduate students.

Covers a wide spectrum of topics on survey, sampling and statistics
An ideal test book for graduate students and researchers in survey sampling theory and applications

Muu info

This broad text provides a comprehensive overview of survey sampling for both basic and advanced survey sampling graduate courses

Preface

xxv

Acknowledgments

xxix

1 Preliminaries and Basics of Probability Sampling

(22)

1.1 Introduction

(1)

1.2 Definitions and Terminologies

(3)

1.2.1 Population and Unit

(1)

1.2.2 Finite and Infinite Populations

(1)

1.2.3 Sampling Frame

(1)

1.2.4 Parameter and Parameter Space

(1)

1.2.5 Complete Enumeration and Sample Survey

(1)

1.2.6 Sampling and Nonsampling Errors

(1)

1.2.7 Sample

(1)

1.2.8 Probability and Purposive Sampling

(1)

1.3 Sampling Design and Inclusion Probabilities

(3)

1.3.1 Sampling Design

(1)

1.3.2 Inclusion Probabilities

(1)

1.3.3 Consistency Conditions of Inclusion Probabilities

(1)

1.3.4 Fixed Effective Size Design

(1)

1.3.5 Fixed Sample Size Design

(1)

1.4 Methods of Selection of Sample

(4)

1.4.1 Cumulative Total Method

(1)

1.4.2 Sampling Scheme

(1)

1.4.3 With and Without Replacement Sampling

(1)

1.4.4 Simple Random Sampling With Replacement

(1)

1.4.5 Simple Random Sampling Without Replacement

(1)

1.4.6 Probability Proportional to Size With Replacement Sampling

(1)

1.4.7 Probability Proportional to Size Without Replacement Sampling

(1)

1.4.8 Lahiri---Midzuno---Sen Sampling Scheme

(1)

1.5 Hanurav's Algorithm

(5)

1.6 Ordered and Unordered Sample

(1)

1.7 Data

(1)

1.7.1 Sample Space

(1)

1.8 Sampling From Hypothetical Populations

(1)

1.8.1 Sampling From a Uniform Population

(1)

1.8.2 Sampling From a Normal Population

(1)

1.8.3 Sampling From a Binomial Population

(1)

1.9 Exercises

(4)

2 Unified Sampling Theory: Design-Based Inference

(28)

2.1 Introduction

(1)

2.2 Definitions and Terminologies

(2)

2.2.1 Noninformative and Adaptive (Sequential) Sampling Designs

(1)

2.2.2 Estimator and Estimate

(1)

2.2.3 Unbiased Estimator

(1)

2.2.4 Mean Square Error and Variance

(1)

2.2.5 Uniformly Minimum Variance Unbiased Estimator

(1)

2.3 Linear Unbiased Estimators

(4)

2.3.1 Conditions of Unbiasedness

(1)

2.3.2 Horvitz--Thompson Estimator

(1)

2.3.3 Hansen--Hurwitz Estimator

(1)

2.3.4 Unbiased Ratio Estimator

(1)

2.3.5 Difference and Generalized Difference Estimator

(1)

2.4 Properties of the Horvitz--Thompson Estimator

(3)

2.5 Nonexistence Theorems

(5)

2.5.1 Unicluster Sampling Design

(1)

2.5.2 Class of Linear Homogeneous Unbiased Estimators

(2)

2.5.3 Optimality of the Horvitz--Thompson Estimator

(1)

2.5.4 Class of All Unbiased Estimators

(1)

2.5.5 Class of Linear Unbiased Estimators

(1)

2.6 Admissible Estimators

(4)

2.7 Sufficiency in Finite Population

(6)

2.7.1 Sufficiency and Likelihood

(3)

2.7.2 Minimal Sufficient Statistic

(1)

2.7.3 Rao--Blackwellization

(2)

2.8 Sampling Strategies

(1)

2.8.1 Unbiased Strategy

(1)

2.8.2 Uniformly Minimum Variance Unbiased Strategy

(1)

2.8.3 Admissible Strategies

(1)

2.8.4 Minimax Strategy

(1)

2.9 Discussions

(1)

2.10 Exercises

(2)

3 Simple Random Sampling

(38)

3.1 Introduction

(1)

3.2 Simple Random Sampling Without Replacement

(17)

3.2.1 Sampling Scheme

(1)

3.2.2 Estimation of Population Mean and Variance

(7)

3.2.3 Estimation of Population Covariance

(2)

3.2.4 Estimation of Population Proportion

(1)

3.2.5 Estimation of Domain Mean and Total

(6)

3.3 Simple Random Sampling With Replacement

(6)

3.3.1 Sampling Scheme

(1)

3.3.2 Estimation of the Population Mean and Variance

(1)

3.3.3 Estimation of Population Proportion

(2)

3.3.4 Rao---Blackwellization

(3)

3.4 Interval Estimation

(2)

3.4.1 Confidence Intervals for Mean and Proportion

(1)

3.4.1.1 Large Sample Size

(1)

3.4.1.2 Small Sample Size

(1)

3.5 Determination of Sample Size

(5)

3.5.1 Consideration of the Cost of a Survey

(1)

3.5.2 Consideration of the Efficiency of Estimators

(1)

3.5.2.1 Given Variance

(1)

3.5.2.2 Given Coefficient of Variation

(1)

3.5.2.3 Given Margin of Permissible Error

(1)

3.5.3 Use of Chebyshev Inequality

(3)

3.6 Inverse Sampling

(3)

3.6.1 Simple Random Sampling Without Replacement

(2)

3.6.2 Simple Random Sampling With Replacement

(1)

3.7 Exercises

(5)

4 Systematic Sampling

(28)

4.1 Introduction

(1)

4.2 Linear Systematic Sampling

(4)

4.2.1 Linear Systematic Sampling With N/n = k an Integer

(1)

4.2.2 Linear Systematic Sampling With N/n = k Not an Integer

(1)

4.2.3 Estimation of the Population Mean and Its Variance

(2)

4.2.4 Nonexistence of Unbiased Variance Estimator

(1)

4.3 Efficiency of Systematic Sampling

(10)

4.3.1 Comparison With Simple Random Sampling

(1)

4.3.2 Comparison With Stratified Sampling

(1)

4.3.3 Random Arrangement of Units

(1)

4.3.4 Population With Linear Trend

(1)

4.3.4.1 End Corrections

(1)

4.3.4.2 Balanced Systematic Sampling

(1)

4.3.5 Population With Periodic Variation

(1)

4.3.6 Autocorrelated Population

(4)

4.4 Linear Systematic Sampling Using Fractional Interval

103

(1)

4.5 Circular Systematic Sampling

103

(3)

4.5.1 Circular Systematic Sampling With k = N/n as an Integer

104

(1)

4.5.2 Circular Systematic Sampling With N/n is Not an Integer

104

(2)

4.6 Variance Estimation

106

(6)

4.6.1 Single Systematic Sample

106

(1)

4.6.1.1 Random Arrangements of Units

106

(1)

4.6.1.2 Stratified Sampling With One Unit Per Stratum

107

(1)

4.6.1.3 Presence of Linear Trend

107

(1)

4.6.1.4 Presence of Autocorrelation Between Successive Units

108

(1)

4.6.1.5 Splitting of a Systematic Sample

108

(1)

4.6.2 Several Systematic Samples

109

(3)

4.7 Two-Dimensional Systematic Sampling

112

(2)

4.8 Exercises

114

(3)

5 Unequal Probability Sampling

117

(50)

5.1 Introduction

117

(1)

5.2 Probability Proportional to Size With Replacement Sampling Scheme

118

(6)

5.2.1 Cumulative Total Method

118

(1)

5.2.2 Lahiri's Method

119

(1)

5.2.3 Hansen---Hurwitz Estimator and its Variance

120

(3)

5.2.4 Rao-Blackwellization

123

(1)

5.3 Probability Proportional to Size Without Replacement Sampling Scheme

124

(12)

5.3.1 Raj's Estimator and its Variance

125

(4)

5.3.2 Rao-Blackwellization

129

(1)

5.3.2.1 Murthy's Estimator

129

(7)

5.4 Inclusion Probability Proportional to Measure of Size Sampling Scheme

136

(16)

5.4.1 Inclusion Probability Proportional to Measure of Size Sampling With n = 2

137

(1)

5.4.1.1 Brewer's Sampling Scheme

137

(1)

5.4.1.2 Durbin's Sampling Scheme

138

(1)

5.4.1.3 Hanurav's Sampling Scheme

139

(1)

5.4.2 Inclusion Probability Proportional to Measure of Size Sampling with n < 2

140

(1)

5.4.2.1 Lahiri--Midzuno---Sen Sampling Design

140

(1)

5.4.2.2 Probability Proportionate to Size Systematic Sampling Scheme

141

(2)

5.4.2.3 Sampford's Sampling Scheme

143

(1)

5.4.2.3.1 Comparison of Efficiency

144

(3)

5.4.2.4 Poisson (or Bernoulli) Sampling

147

(1)

5.4.2.5 Use of Combinatorics

147

(3)

5.4.2.6 The Nearest Proportional to Size Sampling

150

(2)

5.5 Probability Proportional to Aggregate Size Without Replacement

152

(3)

5.6 Rao---Hartley---Cochran Sampling Scheme

155

(6)

5.7 Comparison of Unequal (Varying) Probability Sampling Designs

161

(1)

5.8 Exercises

162

(5)

6 Inference Under Superpopulation Model

167

(46)

6.1 Introduction

167

(1)

6.2 Definitions

168

(2)

6.2.1 Sampling Strategy

168

(1)

6.2.2 Noninformative Sampling Design

168

(1)

6.2.3 Design-Unbiased (or ρ-Unbiased) Estimator

168

(1)

6.2.4 Model-Unbiased (or ξ-Unbiased) Estimator

168

(1)

6.2.5 Model Design---Unbiased (or ρξ-Unbiased) Estimator

168

(1)

6.2.6 Design-Based Inference

169

(1)

6.2.7 Model-Based Inference

169

(1)

6.2.8 Model-Assisted Inference

169

(1)

6.2.9 Optimal Estimator

170

(1)

6.2.10 Optimal Strategy

170

(1)

6.3 Model-Assisted Inference

170

(14)

6.3.1 Optimal Design-Unbiased Predictors

170

(1)

6.3.1.1 Product Measure Model

170

(6)

6.3.1.2 Equicorrelation Model

176

(3)

6.3.1.3 Transformation Model

179

(1)

6.3.2 Optimal Model Design--Unbiased Prediction

180

(2)

6.3.3 Exchangeable Model

182

(1)

6.3.4 Random Permutation Model

183

(1)

6.4 Model-Based Inference

184

(11)

6.4.1 Optimal Model---Unbiased Prediction

186

(1)

6.4.1.1 Product Measure Model

186

(2)

6.4.1.1.1 Optimal Strategy and Purposive Sampling Design

188

(2)

6.4.1.2 Transformation Model

190

(2)

6.4.1.3 Multiple Regression Model

192

(3)

6.5 Robustness of Designs and Predictors

195

(5)

6.5.1 Robustness of Predictors

195

(1)

6.5.2 Balanced Sampling Design

196

(1)

6.5.3 Polynomial Regression Model

197

(1)

6.5.4 Balanced Sample of Order k

198

(1)

6.5.5 Optimality of Balanced Sampling

199

(1)

6.6 Bayesian Inference

200

(4)

6.6.1 Bayes Estimator

202

(2)

6.7 Comparison of Strategies Under Superpopulation Models

204

(6)

6.7.1 Hansen--Hurwitz Strategy With Others

206

(1)

6.7.2 Horvitz-Thompson and Rao---Hartley---Cochran Strategy

207

(1)

6.7.3 Horvitz--Thompson and LahirTHvlidzuno---Sen Strategy

207

(1)

6.7.4 Rao---Hartley---Cochran and Lahiri---Midzuno---Sen Strategy

207

(3)

6.8 Discussions

210

(1)

6.9 Exercises

211

(2)

7 Stratified Sampling

213

(44)

7.1 Introduction

213

(1)

7.2 Definition of Stratified Sampling

213

(1)

7.3 Advantages of Stratified Sampling

214

(1)

7.4 Estimation Procedure

214

(6)

7.4.1 Estimation of Population Mean

215

(2)

7.4.1.1 Arbitrary Fixed Sample Size Design

217

(1)

7.4.1.2 Simple Random Sampling Without Replacement

217

(1)

7.4.1.3 Probability Proportional to Size With Replacement Sampling

218

(1)

7.4.1.4 Simple Random Sampling With Replacement

218

(1)

7.4.2 Estimation of Population Proportion

219

(1)

7.4.2.1 Simple Random Sampling Without Replacement

219

(1)

7.4.2.2 Simple Random Sampling With Replacement

219

(1)

7.4.3 Interval Estimation

220

(1)

7.5 Allocation of Sample Size

220

(5)

7.5.1 Optimum Allocation for Fixed Cost

221

(1)

7.5.2 Optimum Allocation for Fixed Variance

222

(1)

7.5.3 Simple Random Sampling Without Replacement

223

(1)

7.5.4 Simple Random Sampling With Replacement

223

(1)

7.5.5 Probability Proportional to Size With Replacement Sampling

224

(1)

7.5.6 Neyman Optimum Allocation

224

(1)

7.5.7 Proportional Allocation

225

(1)

7.6 Comparison Between Stratified and Unstratified Sampling

225

(8)

7.6.1 Simple Random Sampling Without Replacement

225

(1)

7.6.2 Probability Proportional to Size With Replacement Sampling

226

(2)

7.6.3 Inclusion Probability Proportional to Size Sampling Scheme

228

(5)

7.7 Construction of Strata

233

(7)

7.7.1 Optimum Points of Stratification

233

(1)

7.7.1.1 Proportional Allocation

234

(2)

7.7.1.2 Optimum Allocation

236

(1)

7.7.2 Dalenius and Hodges's Approximation

237

(2)

7.7.3 Other Methods

239

(1)

7.8 Estimation of Gain Due To Stratification

240

(7)

7.8.1 Simple Random Sampling Without Replacement

242

(1)

7.8.2 Probability Proportional to Size With Replacement Sampling

243

(4)

7.9 Poststratification

247

(2)

7.10 Exercises

249

(8)

8 Ratio Method of Estimation

257

(30)

8.1 Introduction

257

(1)

8.2 Ratio Estimator for Population Ratio

257

(7)

8.2.1 Exact Expression of Bias and Mean-Square Error

258

(3)

8.2.2 Approximate Expression of Bias and Mean-Square Errors

261

(3)

8.3 Ratio Estimator for Population Total

264

(2)

8.3.1 Efficiency of the Ratio Estimator

265

(1)

8.3.2 Optimality of the Ratio Estimator

266

(1)

8.4 Biases and Mean-Square Errors for Specific Sampling Designs

266

(4)

8.4.1 Fixed Effective Sample Size (n) Design

266

(1)

8.4.2 Simple Random Sampling Without Replacement

267

(1)

8.4.3 Probability Proportional to Size With Replacement

268

(1)

8.4.4 Simple Random Sampling With Replacement

269

(1)

8.5 Interval Estimation

270

(3)

8.6 Unbiased Ratio, Almost Unbiased Ratio, and Unbiased Ratio---Type Estimators

273

(2)

8.6.1 Unbiased Ratio estimator

273

(1)

8.6.2 Almost Unbiased Ratio Estimator

273

(1)

8.6.3 Unbiased Ratio---Type Estimators

274

(1)

8.6.4 Hartley--Ross Estimator

275

(1)

8.7 Ratio Estimator for Stratified Sampling

275

(6)

8.7.1 Separate Ratio Estimator

276

(1)

8.7.2 Combined Ratio Estimator

277

(1)

8.7.3 Comparison Between the Separate and Combined Ratio Estimators

277

(4)

8.8 Ratio Estimator for Several Auxiliary Variables

281

(2)

8.8.1 Simple Random Sampling Without Replacement

282

(1)

8.9 Exercises

283

(4)

9 Regression, Product, and Calibrated Methods of Estimation

287

(38)

9.1 Introduction

287

(1)

9.2 Difference Estimator

287

(2)

9.3 Regression Estimator

289

(17)

9.3.1 Exact Expression of Bias

289

(1)

9.3.2 Approximate Expression of Bias

290

(1)

9.3.2.1 Bias Under Simple Random Sampling Without Replacement

290

(1)

9.3.3 Approximate Expression of the Mean Square Error

291

(1)

9.3.4 Mean Square Errors for Some Sampling Designs

292

(1)

9.3.4.1 Arbitrary Fixed Effective Sample Size Design

292

(1)

9.3.4.2 Simple Random Sampling Without Replacement

293

(1)

9.3.5 Efficiency of Regression Estimator

294

(1)

9.3.5.1 Comparison With the Ratio Estimator

294

(1)

9.3.6 Optimality of the Regression Estimator

294

(2)

9.3.7 Unbiased Regression Estimator

296

(1)

9.3.7.1 Singh and Srivastava Sampling Scheme

296

(1)

9.3.8 Stratified Regression Estimator

297

(1)

9.3.8.1 Separate Regression Estimator

297

(2)

9.3.8.2 Combined Regression Estimator

299

(2)

9.3.8.3 Comparison Between Combined and Separate Regression Estimators

301

(2)

9.3.9 Regression Estimator for Several Auxiliary Variables

303

(1)

9.3.9.1 Multivariate Regression Estimator

304

(1)

9.3.9.2 Two Auxiliary Variables

305

(1)

9.3.9.3 Raj's Regression Estimator

305

(1)

9.4 Product Method of Estimation

306

(5)

9.4.1 Bias of the Product Estimator

306

(1)

9.4.2 Mean Square Error of the Product Estimator

307

(1)

9.4.3 Comparison With the Conventional Estimator

307

(1)

9.4.4 Product Estimator for a Few Sampling Designs

307

(1)

9.4.4.1 Fixed Effective Sample Size Design

307

(1)

9.4.4.2 Simple Random Sampling Without Replacement

308

(1)

9.4.5 Unbiased Product Type Estimators

308

(2)

9.4.5.1 Simple Random Sampling Without Replacement

310

(1)

9.5 Comparison Between the Ratio, Regression, Product, and Conventional Estimators

311

(1)

9.6 Dual to Ratio Estimator

311

(2)

9.6.1 Bias of the Dual Estimator

312

(1)

9.6.2 Mean Square Error of the Dual Estimator

312

(1)

9.6.3 Comparison With Other Estimators

313

(1)

9.6.3.1 Conventional Estimator

313

(1)

9.6.3.2 Ratio Estimator

313

(1)

9.6.3.3 Product Estimator

313

(1)

9.7 Calibration Estimators

313

(6)

9.7.1 Efficiency of Calibrated Estimator

316

(1)

9.7.2 Calibration Estimator for Several Auxiliary Variables

317

(2)

9.8 Exercises

319

(6)

Appendix 9A

322

(3)

10 Two-Phase Sampling

325

(42)

10.1 Introduction

325

(1)

10.2 Two-Phase Sampling for Estimation

326

(19)

10.2.1 Difference Method of Estimation

326

(1)

10.2.1.1 Arbitrary Sampling Design

327

(1)

10.2.1.2 Simple Random Sampling Without Replacement

328

(1)

10.2.1.3 Efficiency Under Simple Random Sampling Without Replacement

329

(1)

10.2.1.4 Probability Proportional to Size With Replacement Sampling

330

(1)

10.2.2 Ratio Method of Estimation

331

(1)

10.2.2.1 Approximate Expression of Bias

332

(2)

10.2.2.2 Approximate Expression of Mean Square Error

334

(1)

10.2.2.3 Simple Random Sampling Without Replacement

335

(1)

10.2.2.4 Optimal Allocation Under Simple Random Sampling Without Replacement

336

(1)

10.2.3 Regression Method of Estimation

337

(1)

10.2.3.1 Approximate Expressions of Bias and Mean Square Errors

337

(1)

10.2.3.2 Arbitrary Sampling Design

338

(2)

10.2.3.3 Simple Random Sampling Without Replacement

340

(2)

10.2.3.4 Optimum Allocation

342

(3)

10.3 Two-Phase Sampling for Stratification

345

(9)

10.3.1 Estimation of Mean and Variance

345

(4)

10.3.2 Proportional Allocation

349

(1)

10.3.3 Estimation of Proportion

350

(1)

10.3.4 Optimum Allocation of Sample Sizes

351

(3)

10.4 Two-Phase Sampling for Selection of Sample

354

(4)

10.4.1 Probability Proportional to Size With Replacement Sampling

354

(2)

10.4.2 Rao---Hartley---Cochran Sampling

356

(2)

10.5 Two-Phase Sampling for Stratification and Selection of Sample

358

(4)

10.6 Exercises

362

(5)

11 Repetitive Sampling

367

(42)

11.1 Introduction

367

(1)

11.2 Estimation of Mean for the Most Recent Occasion

368

(26)

11.2.1 Sampling on Two Occasions

368

(1)

11.2.1.1 Sampling Scheme

368

(1)

11.2.1.2 General Method of Estimation

368

(3)

11.2.1.3 Simple Random Sampling Without Replacement

371

(4)

11.2.1.3.1 Optimum Allocation of the Matched Sample

375

(3)

11.2.1.4 Probability Proportional to Size With Replacement Sampling

378

(3)

11.2.1.5 Simple Random Sampling With Replacement

381

(1)

11.2.1.6 Sampling Over Two Occasions: Stratifying the Initial Sample

381

(6)

11.2.2 Sampling More Than Two Occasions

387

(1)

11.2.2.1 Probability Proportional to Size With Replacement Sampling

387

(2)

11.2.2.1.1 Estimator for the Total on hth Occasion

389

(4)

11.2.2.2 Simple Random Sampling With Replacement

393

(1)

11.2.2.2.1 Estimator for the Total on the hxh Occasion

393

(1)

11.3 Estimation of Change Over Two Occasions

394

(2)

11.3.1 Simple Random Sampling Without Replacement

395

(1)

11.4 Estimation of Mean of Means

396

(6)

11.4.1 Simple Random Sampling Without Replacement

397

(5)

11.5 Exercises

402

(7)

12 Cluster Sampling

409

(14)

12.1 Introduction

409

(1)

12.2 Estimation of Population Total and Variance

410

(3)

12.2.1 Arbitrary Sampling Design

411

(1)

12.2.2 Simple Random Sampling Without Replacement

412

(1)

12.3 Efficiency of Cluster Sampling

413

(3)

12.3.1 Optimum Choice of Cluster Size

414

(2)

12.4 Probability Proportional to Size With Replacement Sampling

416

(1)

12.4.1 Simple Random Sampling With Replacement

417

(1)

12.5 Estimation of Mean per Unit

417

(3)

12.5.1 Examples

419

(1)

12.5.1.1 Arbitrary Sampling Design

419

(1)

12.5.1.2 Simple Random Sampling Without Replacement

419

(1)

12.6 Exercises

420

(3)

13 Multistage Sampling

423

(30)

13.1 Introduction

423

(1)

13.2 Two-Stage Sampling Scheme

424

(1)

13.3 Estimation of the Population Total and Variance

424

(6)

13.3.1 First-Stage Arbitrary Sampling Designs and Second-Stage Simple Random Sampling Without Replacement

427

(1)

13.3.2 Simple Random Sampling Without Replacement Both the Stages

428

(1)

13.3.3 First-Stage Rao-Hartley-Cochran and Second-Stage Simple Random Sampling Without Replacement

429

(1)

13.4 First-Stage Units Are Selected by PPSWR Sampling Scheme

430

(5)

13.4.1 Simple Random Sampling With Replacement

431

(1)

13.4.2 Raj Estimator for Multi-Stage Sampling

432

(3)

13.5 Modification of Variance Estimators

435

(2)

13.5.1 Srinath and Hidiroglou Modification

435

(1)

13.5.2 Arnab Modification

436

(1)

13.6 More than Two-Stage Sampling

437

(2)

13.6.1 Three-Stage Sampling

438

(1)

13.7 Estimation of Mean per Unit

439

(2)

13.7.1 Simple Random Sampling Without Replacement

441

(1)

13.8 Optimum Allocation

441

(3)

13.8.1 Fixed Expected Cost

442

(1)

13.8.2 Fixed Variance

443

(1)

13.9 Self-weighting Design

444

(4)

13.10 Exercises

448

(5)

14 Variance/Mean Square Estimation

453

(16)

14.1 Introduction

453

(1)

14.2 Linear Unbiased Estimators

453

(3)

14.2.1 Conditions of Unbiased Estimation of Variance

454

(2)

14.3 Nonnegative Variance/Mean Square Estimation

456

(9)

14.3.1 Examples

459

(1)

14.3.1.1 Horvitz--Thompson Estimator

459

(1)

14.3.1.2 Hansen--Hurwitz Estimator

460

(1)

14.3.1.3 Murthy's Estimator

461

(1)

14.3.1.4 Unbiased Ratio Estimator

462

(1)

14.3.1.5 Ordinary Ratio Estimator

463

(1)

14.3.1.6 Hartley--Ross Estimator

464

(1)

14.4 Exercises

465

(4)

15 Nonsampling Errors

469

(36)

15.1 Introduction

469

(1)

15.2 Sources of Nonsampling Errors

469

(2)

15.3 Controlling of Nonsampling Errors

471

(1)

15.4 Treatment of Nonresponse Error

471

(22)

15.4.1 Poststratification

472

(1)

15.4.1.1 Hansen--Hurwitz Method

472

(1)

15.4.1.1.1 Optimum Value of v and n

473

(2)

15.4.2 Use of Response Probabilities

475

(1)

15.4.2.1 Classification of Response Probabilities

475

(1)

15.4.3 Politz and Simmons Method

476

(3)

15.4.4 Imputation

479

(2)

15.4.4.1 Problems of Imputation

481

(2)

15.4.5 Multiple Imputation

483

(1)

15.4.6 Bayesian Imputation

484

(1)

15.4.6.1 Wang et al. Method

485

(2)

15.4.6.2 Schenker and Welsh Method

487

(1)

15.4.7 Subsampling Method

488

(1)

15.4.7.1 Arnab and Singh Method

488

(2)

15.4.7.1.1 Simple Random Sampling Without Replacement

490

(1)

15.4.7.2 Singh and Singh Method

491

(2)

15.5 Measurement Error

493

(9)

15.5.1 Measurement Bias and Variance

493

(2)

15.5.1.1 Simple Random Sampling Without Replacement

495

(1)

15.5.2 Interpenetrating Subsamples

496

(6)

15.6 Exercises

502

(3)

16 Randomized Response Techniques

505

(52)

16.1 Introduction

505

(1)

16.2 Randomized Response Techniques for Qualitative Characteristics

506

(7)

16.2.1 Warner's Technique: the Pioneering Method

506

(1)

16.2.1.1 Estimation of Proportion

506

(1)

16.2.1.2 Comparison With Direct Response Surveys

507

(1)

16.2.1.3 Maximum Likelihood Estimation of Proportion

508

(1)

16.2.2 Greenberg et al.: Unrelated Question Method

509

(1)

16.2.2.1 Estimation of Proportion

509

(2)

16.2.3 Kuk's Model

511

(1)

16.2.4 Mangat and Singh Model

512

(1)

16.3 Extension to More Than One Categories

513

(2)

16.3.1 Liu and Chow's Technique

513

(1)

16.3.1.1 Estimation of Proportions

514

(1)

16.4 Randomized Response Techniques for Quantitative Characteristics

515

(5)

16.4.1 Eriksson's Technique

515

(1)

16.4.2 Arnab's Model

516

(2)

16.4.3 Christofides's Model

518

(1)

16.4.4 Eichhorn and Hayre's Model

518

(1)

16.4.5 Franklin's Randomized Response Technique

519

(1)

16.4.6 Chaudhuri's Randomized Response

520

(1)

16.5 General Method of Estimation

520

(13)

16.5.1 Estimation of Total and Variance

521

(2)

16.5.1.1 Horvitz---Thomson Estimator

523

(1)

16.5.1.2 Simple Random Sampling Without Replacement

524

(1)

16.5.1.3 Rao---Hartley---Cochran Sampling

525

(2)

16.5.1.4 Probability Proportional to Aggregate Size Sampling

527

(1)

16.5.1.5 Probability Proportional to Size With Replacement Sampling

528

(2)

16.5.1.6 Simple Random Sampling With Replacement

530

(3)

16.6 Optional Randomized Response Techniques

533

(6)

16.6.1 Full Optional Randomized Response Technique

533

(1)

16.6.1.1 Estimation of Population Total

534

(1)

16.6.1.2 Horvitz--Thompson Estimator Based on a Fixed Sample Size Design

535

(1)

16.6.1.3 Simple Random Sampling Without Replacement

536

(1)

16.6.1.4 Rao---Hartley---Cochran Sampling

536

(1)

16.6.1.5 Probability Proportional to Size With Replacement Sampling

537

(1)

16.6.1.6 Simple Random Sampling With Replacement

537

(1)

16.6.2 Partial Optional Randomized Response Technique

537

(1)

16.6.2.1 Gupta et al. Model

538

(1)

16.7 Measure of Protection of Privacy

539

(9)

16.7.1 Qualitative Characteristic With "Yes-No" Response

539

(1)

16.7.1.1 Leysieffer and Warner's Measure

539

(5)

16.7.1.2 Lanke's Measure

544

(1)

16.7.1.3 Anderson's Measure

545

(1)

16.7.2 Quantitative Characteristics

546

(2)

16.8 Optimality Under Superpopulation Model

548

(5)

16.8.1 Product Measure Model

549

(1)

16.8.2 Equicorrelation Model

550

(2)

16.8.3 Construction of an Optimal Randomized Response Technique

552

(1)

16.9 Exercises

553

(4)

17 Domain and Small Area Estimation

557

(30)

17.1 Introduction

557

(1)

17.2 Domain Estimation

558

(2)

17.2.1 Horvitz---Thomson Estimator

559

(1)

17.3 Small Area Estimation

560

(23)

17.3.1 Symptomatic Accounting Technique

561

(1)

17.3.1.1 Vital Rates Method

561

(1)

17.3.1.2 Composite Method

562

(1)

17.3.1.3 Census Component Method

562

(1)

17.3.1.4 Housing Unit Method

562

(1)

17.3.1.5 Ratio Correlation Method

562

(1)

17.3.1.6 Difference Correlation Method

563

(1)

17.3.2 Direct Estimation

564

(1)

17.3.3 Synthetic Estimation

564

(2)

17.3.4 Composite Estimation

566

(1)

17.3.5 Borrowing Strength From Related Areas

567

(1)

17.3.5.1 Synthetic Estimator

568

(1)

17.3.5.2 Generalized Regression Estimator

568

(1)

17.3.5.3 Composite Estimator

568

(5)

17.3.6 Use of Models

573

(1)

17.3.6.1 General Linear Mixed Model

573

(2)

17.3.6.2 Nested Error Regression Model

575

(2)

17.3.6.3 Area-Level Model

577

(2)

17.3.6.4 Fay--Herriot Model

579

(1)

17.3.7 Empirical Best Linear Unbiased Prediction, Empirical Bayes, and Hierarchical Bayes Methods

580

(1)

17.3.7.1 Empirical Best Linear Unbiased Prediction

580

(1)

17.3.7.1.1 Onefold Nested Error Regression Model

580

(1)

17.3.7.1.2 Fay--Herriot Model

581

(1)

17.3.7.2 Empirical Bayes Approach

581

(1)

17.3.7.3 Hierarchical Bayes Approach

582

(1)

17.4 Exercises

583

(4)

18 Variance Estimation: Complex Survey Designs

587

(58)

18.1 Introduction

587

(1)

18.2 Linearization Method

587

(5)

18.2.1 Ratio Estimator

589

(2)

18.2.2 Coefficient of Variation

591

(1)

18.3 Random Group Method

592

(7)

18.3.1 Simple Random Sampling With Replacement

593

(1)

18.3.2 Simple Random Sampling Without Replacement

594

(1)

18.3.3 Varying Probability Sampling

595

(1)

18.3.4 Multistage Sampling

596

(2)

18.3.5 Numerical Example

598

(1)

18.4 Jackknife Method

599

(15)

18.4.1 Jackknife Method for an Infinite Population

600

(4)

18.4.1.1 Higher-Order Jackknife Estimator

604

(1)

18.4.1.2 Generalized Jackknife Estimator

605

(1)

18.4.2 Jackknife Method for a Finite Population

606

(1)

18.4.2.1 Probability Proportional to Size With Replacement Sampling

606

(1)

18.4.2.1.1 Bias of Jackknife Variance Estimator

607

(1)

18.4.2.2 Simple Random Sampling With Replacement

608

(1)

18.4.2.3 Inclusion Probability Proportional to Size or πρs Sampling Design

608

(1)

18.4.2.3.1 Bias of Jackknife Variance Estimator

609

(1)

18.4.2.4 Simple Random Sampling Without Replacement

610

(1)

18.4.2.5 Regression Estimator

610

(1)

18.4.2.6 Numerical Example

611

(3)

18.5 Balanced Repeated Replication Method

614

(15)

18.5.1 Stratified Sampling With nh = 2

614

(5)

18.5.2 Methods of Variance Estimation

619

(1)

18.5.3 Applications

620

(1)

18.5.3.1 Population Ratio

620

(1)

18.5.3.2 Inclusion Probability Proportional to Size Sampling Scheme

621

(1)

18.5.4 Numerical Example

622

(1)

18.5.4.1 Population Mean

622

(1)

18.5.4.2 Population Ratio

623

(1)

18.5.4.3 Correlation Coefficient

624

(1)

18.5.5 Stratum Size nh ≥ 2

625

(1)

18.5.5.1 Grouped Balanced Half-Sample Method

625

(1)

18.5.5.2 Subdivision of Strata

626

(1)

18.5.6 Stratified Multistage Sampling

627

(1)

18.5.7 Fay's Method

628

(1)

18.6 Bootstrap Method

629

(8)

18.6.1 Bootstrap for Infinite Population

629

(1)

18.6.1.1 Bootstrap Confidence Interval

630

(1)

18.6.1.1.1 Percentile Method

630

(1)

18.6.1.1.2 Bootstrap t-Method

630

(1)

18.6.2 Bootstrap for Finite Population

630

(1)

18.6.2.1 Bootstrap for Simple Random Sampling With Replacement

631

(2)

18.6.2.2 Rescaling Bootstrap

633

(2)

18.6.2.3 Bootstrap Without Replacement Method

635

(1)

18.6.2.4 Mirror-Match Bootstrap

635

(1)

18.6.2.5 Bootstrap for Varying Probability Sampling Without Replacement

636

(1)

18.7 Generalized Variance Functions

637

(3)

18.7.1 Generalized Variance Function Model

637

(1)

18.7.2 Justification of Generalized Variance Function Model

638

(1)

18.7.3 Generalized Variance Function Method for Variance Estimation

639

(1)

18.7.4 Applicability Generalized Variance Function Model

640

(1)

18.8 Comparison Between the Variance Estimators

640

(1)

18.9 Exercises

641

(4)

19 Complex Surveys: Categorical Data Analysis

645

(28)

19.1 Introduction

645

(1)

19.2 Pearsonian Chi-Square Test for Goodness of Fit

645

(1)

19.3 Goodness of Fit for a General Sampling Design

646

(15)

19.3.1 Wald Statistic for Goodness of Fit

649

(1)

19.3.1.1 Simple Random Sampling With Replacement

649

(1)

19.3.2 Generalized Pearsonian Chi-Square Statistic

650

(1)

19.3.2.1 Design Effect

651

(1)

19.3.3 Modifications to X2G

651

(1)

19.3.3.1 Use of Maximum or Minimum Eigenvalues

651

(1)

19.3.3.2 Rao--Scott First-Order Corrections

652

(1)

19.3.3.3 Rao--Scott Second-Order Corrections

653

(1)

19.3.3.4 Fellegi Correction

653

(1)

19.3.4 Simple Random Sampling Without Replacement

654

(1)

19.3.5 Stratified Sampling

654

(1)

19.3.6 Two-Stage Sampling

655

(3)

19.3.7 Residual Analysis

658

(3)

19.4 Test of Independence

661

(2)

19.4.1 Wald Statistic

661

(1)

19.4.2 Bonferroni Test

662

(1)

19.4.3 Modified Chi-Square

662

(1)

19.5 Tests of Homogeneity

663

(1)

19.5.1 Wald Statistic

663

(1)

19.5.2 Modified Chi-Square Statistics

664

(1)

19.6 Chi-Square Test Based on Superpopulation Model

664

(3)

19.6.1 Altham's Model

664

(3)

19.6.1.1 A Simpler Model

667

(1)

19.6.2 Brier Model

667

(1)

19.7 Concluding Remarks

667

(1)

19.8 Exercises

668

(5)

20 Complex Survey Design: Regression Analysis

673

(18)

20.1 Introduction

673

(1)

20.2 Design-Based Approach

674

(6)

20.2.1 Estimation of Variance

677

(2)

20.2.2 Logistic Regression

679

(1)

20.3 Model-Based Approach

680

(7)

20.3.1 Performances of the Proposed Estimators

681

(1)

20.3.2 Variance Estimation

681

(1)

20.3.3 Multistage Sampling

682

(3)

20.3.4 Separate Regression for Each First-Stage Unit

685

(2)

20.4 Concluding Remarks

687

(1)

20.5 Exercises

687

(4)

21 Ranked Set Sampling

691

(32)

21.1 Introduction

691

(1)

21.2 Ranked Set Sampling by Simple Random Sampling With Replacement Method

691

(17)

21.2.1 A Fundamental Equality

692

(1)

21.2.2 Estimation of the Mean

693

(2)

21.2.3 Precision of the Ranked Set Sampling

695

(1)

21.2.4 Optimum Value of m

696

(2)

21.2.5 Optimum Allocation

698

(1)

21.2.5.1 Right-Tail Allocation Model

699

(1)

21.2.6 Judgment Ranking

700

(1)

21.2.6.1 Moment of the Judgment Order Statistic

700

(1)

21.2.7 Estimation of Population Variance

701

(1)

21.2.7.1 Efficiency of σ2(rss)

702

(1)

21.2.8 Use of Concomitant Variables

703

(5)

21.2.8.1 Relative Precision of μreg

708

(1)

21.3 Simple Random Sampling Without Replacement

708

(8)

21.3.1 Relative Precision

715

(1)

21.4 Size-Biased Probability of Selection

716

(2)

21.5 Concluding Remarks

718

(1)

21.6 Exercises

719

(4)

22 Estimating Functions

723

(24)

22.1 Introduction

723

(1)

22.2 Estimating Function and Estimating Equations

723

(4)

22.2.1 Optimal Properties of Estimating Functions

725

(2)

22.3 Estimating Function from Superpopulation Model

727

(4)

22.3.1 Optimal and Linearly Optimal Estimating Functions

728

(3)

22.4 Estimating Function for a Survey Population

731

(6)

22.5 Interval Estimation

737

(5)

22.5.1 Confidence Interval for θ

737

(1)

22.5.1.1 Confidence Interval for Survey Parameter θN

737

(2)

22.5.1.2 Stratified Sampling

739

(2)

22.5.1.3 Confidence Intervals for Quantiles

741

(1)

22.6 Nonresponse

742

(2)

22.7 Concluding Remarks

744

(1)

22.8 Exercises

745

(2)

23 Estimation of Distribution Functions and Quantiles

747

(26)

23.1 Introduction

747

(1)

23.2 Estimation of Distribution Functions

747

(14)

23.2.1 Design-Based Estimation

748

(1)

23.2.2 Design-Based Estimators Using Auxiliary Information

749

(1)

23.2.3 Model-Based Estimators

750

(2)

23.2.4 Model-Assisted Estimators

752

(2)

23.2.5 Nonparametric Regression Method

754

(1)

23.2.5.1 Nandaraya---Watson Estimator

755

(1)

23.2.5.2 Breidt and Opsomer Estimator

755

(1)

23.2.5.3 Kuo Estimator

756

(1)

23.2.5.4 Kuk Estimator

756

(1)

23.2.6 Calibration Method

757

(2)

23.2.7 Method of Poststratification

759

(1)

23.2.8 Empirical Comparison of the Estimators

760

(1)

23.3 Estimation of Quantiles

761

(1)

23.4 Estimation of Median

762

(5)

23.4.1 Position Estimator and Stratification Estimator

762

(2)

23.4.2 Comparison of the Efficiencies

764

(1)

23.4.3 Further Generalization

765

(1)

23.4.4 Empirical Comparison

766

(1)

23.5 Confidence Interval for Distribution Function and Quantiles

767

(2)

23.6 Concluding Remarks

769

(1)

23.7 Exercises

770

(3)

24 Controlled Sampling

773

(22)

24.1 Introduction

773

(1)

24.2 Pioneering Method

774

(2)

24.3 Experimental Design Configurations

776

(7)

24.3.1 Equal Probability Sampling Design

776

(3)

24.3.2 Unequal Probability Sampling Design

779

(1)

24.3.3 Balanced Sampling Plan Without Contiguous Units

780

(3)

24.4 Application of Linear Programming

783

(1)

24.5 Nearest Proportional to Size Design

784

(1)

24.6 Application of Nonlinear Programming

785

(1)

24.7 Coordination of Samples Overtime

786

(6)

24.7.1 Keyfitz Method

787

(2)

24.7.2 Probability Proportional to Aggregate Size Sampling Scheme

789

(1)

24.7.2.1 Lanke Method

789

(3)

24.8 Discussions

792

(1)

24.9 Exercises

792

(3)

25 Empirical Likelihood Method in Survey Sampling

795

(26)

25.1 Introduction

795

(1)

25.2 Scale Load Approach

795

(2)

25.3 Empirical Likelihood Approach

797

(1)

25.4 Empirical Likelihood for Simple Random Sampling

798

(1)

25.5 Pseudo--empirical Likelihood Method

799

(3)

25.5.1 MPEL Estimator for the Population Mean

801

(1)

25.5.2 MPEL Estimator for the Population Distribution Function

801

(1)

25.5.3 MPEL Estimator Under Linear Constraints

801

(1)

25.6 Asymptotic Behavior of MPEL Estimator

802

(2)

25.6.1 GREG Estimator Versus MPEL Estimator

803

(1)

25.7 Empirical Likelihood for Stratified Sampling

804

(5)

25.7.1 Asymptotic Properties

805

(1)

25.7.1.1 Variance Estimation

806

(1)

25.7.1.2 Jackknife Variance Estimation

807

(1)

25.7.2 Pseudo--empirical Likelihood Estimator

807

(1)

25.7.2.1 Multistage Sampling

808

(1)

25.8 Model-Calibrated Pseudoempirical Likelihood

809

(3)

25.8.1 Estimation of the Population Mean

809

(1)

25.8.2 Estimation of the Population Distribution Function

810

(1)

25.8.3 Model-Calibrated MPEL Estimation for Population Quadratic Parameters

811

(1)

25.9 Pseudo--empirical Likelihood to Raking

812

(1)

25.10 Empirical Likelihood Ratio Confidence Intervals

813

(5)

25.10.1 Simple Random Sampling

813

(1)

25.10.2 Complex Sampling Designs

814

(3)

25.10.3 Stratified Sampling

817

(1)

25.10.4 Confidence Interval for Distribution Function

818

(1)

25.11 Concluding Remarks

818

(1)

25.12 Exercises

819

(2)

26 Sampling Rare and Mobile Populations

821

(38)

26.1 Introduction

821

(1)

26.2 Screening

822

(2)

26.2.1 Telephonic Interview

822

(1)

26.2.2 Mail Questionnaire

822

(1)

26.2.3 Cluster Sampling

823

(1)

26.2.3.1 Sudman--Waksberg Method

823

(1)

26.2.4 Two-Phase Sampling

824

(1)

26.3 Disproportionate Sampling

824

(1)

26.4 Multiplicity or Network Sampling

825

(1)

26.5 Multiframe Sampling

826

(11)

26.5.1 Methods of Estimation

827

(1)

26.5.2 Simple Random Sampling Without Replacement

828

(7)

26.5.3 General Sampling Procedures

835

(1)

26.5.4 Horvitz---Thompson-Based Estimators

836

(1)

26.5.5 Concluding Remarks

837

(1)

26.6 Snowball Sampling

837

(1)

26.7 Location Sampling

838

(1)

26.8 Sequential Sampling

839

(1)

26.9 Adaptive Sampling

840

(4)

26.9.1 Unbiased Estimation of Population Mean

840

(1)

26.9.1.1 Use of Intersection Probabilities

841

(1)

26.9.1.2 Use of the Number of Intersections

842

(2)

26.10 Capture--Recapture Method

844

(12)

26.10.1 Closed Population

844

(1)

26.10.1.1 Peterson and Lincoln Method

844

(1)

26.10.1.2 Hypergeometric Model

845

(1)

26.10.1.3 Bailey's Binomial Model

846

(1)

26.10.1.4 Ratio Method

846

(1)

26.10.1.5 Inverse Sampling Methods

846

(1)

26.10.1.5.1 Without Replacement Method

846

(1)

26.10.1.5.2 With Replacement Method

847

(1)

26.10.1.6 Interval Estimation

848

(1)

26.10.1.7 Multiple Marking

849

(2)

26.10.2 Open Model

851

(1)

26.10.2.1 Jolly--Seber Model

851

(1)

26.10.2.1.1 Summary Data

851

(2)

26.10.2.1.2 Assumptions of the Model

853

(1)

26.10.2.1.3 Estimation of Parameters

853

(3)

26.11 Exercises

856

(3)

References

859

(24)

Author Index

883

(8)

Subject Index

891

Prof. Raghunath Arnab is a Professor of Statistics, University of Botswana, Botswana and Honorary Professor of Statistics, University of KwaZulu-Natal, South Africa. Prof. Arnab received his Ph.D. degree in 1981 from the Indian Statistical Institute, Kolkata. He is a co-author of the book A new concept for tuning design weights in survey sampling (jointly with Prof. S. Singh, Prof. A. Sedory, Prof. M. der Mar Rueda, Prof. A. Arcos) and an author of numerous research articles, Associate editor of the Journal of Statistical Theory and Practice, Model Assisted statistics and its Applications, Journal of the Indian Society of Agricultural Statistics and Advances and Applications in Statistics. Prof. Arnab was an elected member of the International Statistical Institute, Life member of the International Statistical Institute and a member of the Biometric Society.

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