Muutke küpsiste eelistusi

E-raamat: Survey Sampling Theory and Applications

(Department of Statistics, University of Botswana, Botswana, and University of Kwa-Zulu Natal, South Africa)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 08-Mar-2017
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780128118979
Teised raamatud teemal:
  • Formaat - EPUB+DRM
  • Hind: 156,97 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Survey Sampling Theory and ApplicationsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 08-Mar-2017
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780128118979
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

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
1(22)
1.1 Introduction
1(1)
1.2 Definitions and Terminologies
1(3)
1.2.1 Population and Unit
1(1)
1.2.2 Finite and Infinite Populations
2(1)
1.2.3 Sampling Frame
2(1)
1.2.4 Parameter and Parameter Space
2(1)
1.2.5 Complete Enumeration and Sample Survey
3(1)
1.2.6 Sampling and Nonsampling Errors
3(1)
1.2.7 Sample
4(1)
1.2.8 Probability and Purposive Sampling
4(1)
1.3 Sampling Design and Inclusion Probabilities
4(3)
1.3.1 Sampling Design
4(1)
1.3.2 Inclusion Probabilities
5(1)
1.3.3 Consistency Conditions of Inclusion Probabilities
5(1)
1.3.4 Fixed Effective Size Design
6(1)
1.3.5 Fixed Sample Size Design
6(1)
1.4 Methods of Selection of Sample
7(4)
1.4.1 Cumulative Total Method
7(1)
1.4.2 Sampling Scheme
8(1)
1.4.3 With and Without Replacement Sampling
8(1)
1.4.4 Simple Random Sampling With Replacement
9(1)
1.4.5 Simple Random Sampling Without Replacement
9(1)
1.4.6 Probability Proportional to Size With Replacement Sampling
9(1)
1.4.7 Probability Proportional to Size Without Replacement Sampling
10(1)
1.4.8 Lahiri---Midzuno---Sen Sampling Scheme
10(1)
1.5 Hanurav's Algorithm
11(5)
1.6 Ordered and Unordered Sample
16(1)
1.7 Data
17(1)
1.7.1 Sample Space
17(1)
1.8 Sampling From Hypothetical Populations
18(1)
1.8.1 Sampling From a Uniform Population
18(1)
1.8.2 Sampling From a Normal Population
18(1)
1.8.3 Sampling From a Binomial Population
18(1)
1.9 Exercises
19(4)
2 Unified Sampling Theory: Design-Based Inference
23(28)
2.1 Introduction
23(1)
2.2 Definitions and Terminologies
23(2)
2.2.1 Noninformative and Adaptive (Sequential) Sampling Designs
23(1)
2.2.2 Estimator and Estimate
23(1)
2.2.3 Unbiased Estimator
24(1)
2.2.4 Mean Square Error and Variance
24(1)
2.2.5 Uniformly Minimum Variance Unbiased Estimator
25(1)
2.3 Linear Unbiased Estimators
25(4)
2.3.1 Conditions of Unbiasedness
26(1)
2.3.2 Horvitz--Thompson Estimator
27(1)
2.3.3 Hansen--Hurwitz Estimator
28(1)
2.3.4 Unbiased Ratio Estimator
28(1)
2.3.5 Difference and Generalized Difference Estimator
29(1)
2.4 Properties of the Horvitz--Thompson Estimator
29(3)
2.5 Nonexistence Theorems
32(5)
2.5.1 Unicluster Sampling Design
33(1)
2.5.2 Class of Linear Homogeneous Unbiased Estimators
33(2)
2.5.3 Optimality of the Horvitz--Thompson Estimator
35(1)
2.5.4 Class of All Unbiased Estimators
36(1)
2.5.5 Class of Linear Unbiased Estimators
37(1)
2.6 Admissible Estimators
37(4)
2.7 Sufficiency in Finite Population
41(6)
2.7.1 Sufficiency and Likelihood
41(3)
2.7.2 Minimal Sufficient Statistic
44(1)
2.7.3 Rao--Blackwellization
45(2)
2.8 Sampling Strategies
47(1)
2.8.1 Unbiased Strategy
47(1)
2.8.2 Uniformly Minimum Variance Unbiased Strategy
47(1)
2.8.3 Admissible Strategies
47(1)
2.8.4 Minimax Strategy
48(1)
2.9 Discussions
48(1)
2.10 Exercises
49(2)
3 Simple Random Sampling
51(38)
3.1 Introduction
51(1)
3.2 Simple Random Sampling Without Replacement
51(17)
3.2.1 Sampling Scheme
51(1)
3.2.2 Estimation of Population Mean and Variance
52(7)
3.2.3 Estimation of Population Covariance
59(2)
3.2.4 Estimation of Population Proportion
61(1)
3.2.5 Estimation of Domain Mean and Total
62(6)
3.3 Simple Random Sampling With Replacement
68(6)
3.3.1 Sampling Scheme
68(1)
3.3.2 Estimation of the Population Mean and Variance
68(1)
3.3.3 Estimation of Population Proportion
69(2)
3.3.4 Rao---Blackwellization
71(3)
3.4 Interval Estimation
74(2)
3.4.1 Confidence Intervals for Mean and Proportion
74(1)
3.4.1.1 Large Sample Size
74(1)
3.4.1.2 Small Sample Size
75(1)
3.5 Determination of Sample Size
76(5)
3.5.1 Consideration of the Cost of a Survey
76(1)
3.5.2 Consideration of the Efficiency of Estimators
76(1)
3.5.2.1 Given Variance
76(1)
3.5.2.2 Given Coefficient of Variation
77(1)
3.5.2.3 Given Margin of Permissible Error
77(1)
3.5.3 Use of Chebyshev Inequality
78(3)
3.6 Inverse Sampling
81(3)
3.6.1 Simple Random Sampling Without Replacement
81(2)
3.6.2 Simple Random Sampling With Replacement
83(1)
3.7 Exercises
84(5)
4 Systematic Sampling
89(28)
4.1 Introduction
89(1)
4.2 Linear Systematic Sampling
89(4)
4.2.1 Linear Systematic Sampling With N/n = k an Integer
89(1)
4.2.2 Linear Systematic Sampling With N/n = k Not an Integer
90(1)
4.2.3 Estimation of the Population Mean and Its Variance
90(2)
4.2.4 Nonexistence of Unbiased Variance Estimator
92(1)
4.3 Efficiency of Systematic Sampling
93(10)
4.3.1 Comparison With Simple Random Sampling
93(1)
4.3.2 Comparison With Stratified Sampling
94(1)
4.3.3 Random Arrangement of Units
95(1)
4.3.4 Population With Linear Trend
96(1)
4.3.4.1 End Corrections
97(1)
4.3.4.2 Balanced Systematic Sampling
98(1)
4.3.5 Population With Periodic Variation
99(1)
4.3.6 Autocorrelated Population
99(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.
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97801281189796e.html
Märksõnad: