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E-raamat: Introduction to Model-Based Survey Sampling with Applications

(School of Mathematics and Applied Statistics, University of Wollongong, Australia), (School of Mathematics and Applied Statistics, University of Wollongong, Australia)
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Introduction to Model-Based Survey Sampling with ApplicationsSuurem pilt
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This text brings together important ideas on the model-based approach to sample survey, which has been developed over the last twenty years. Suitable for graduate students and professional statisticians, it moves from basic ideas fundamental to sampling to more rigorous mathematical modelling and data analysis and includes exercises and solutions.

This text brings together important ideas on the model-based approach to sample survey, which has been developed over the last twenty years. Suitable for graduate students and professional statisticians, it moves from basic ideas fundamental to sampling to more rigorous mathematical modelling and data analysis and includes exercises and solutions.
Part I Basics Of Model-Based Survey Inference
1 Introduction
3(11)
1.1 Why Sample?
4(1)
1.2 Target Populations and Sampling Frames
5(1)
1.3 Notation
6(3)
1.4 Population Models and Non-Informative Sampling
9(5)
2 The Model-Based Approach
14(4)
2.1 Optimal Prediction
16(2)
3 Homogeneous Populations
18(10)
3.1 Random Sampling Models
19(1)
3.2 A Model for a Homogeneous Population
20(1)
3.3 Empirical Best Prediction and Best Linear Unbiased Prediction of the Population Total
21(2)
3.4 Variance Estimation and Confidence Intervals
23(1)
3.5 Predicting the Value of a Linear Population Parameter
24(1)
3.6 How Large a Sample?
24(2)
3.7 Selecting a Simple Random Sample
26(1)
3.8 A Generalisation of the Homogeneous Model
26(2)
4 Stratified Populations
28(21)
4.1 The Homogeneous Strata Population Model
29(1)
4.2 Optimal Prediction Under Stratification
30(1)
4.3 Stratified Sample Design
31(1)
4.4 Proportional Allocation
31(3)
4.5 Optimal Allocation
34(1)
4.6 Allocation for Proportions
35(1)
4.7 How Large a Sample?
36(1)
4.8 Defining Stratum Boundaries
37(3)
4.9 Model-Based Stratification
40(2)
4.10 Equal Aggregate Size Stratification
42(1)
4.11 Multivariate Stratification
43(2)
4.12 How Many Strata?
45(4)
5 Populations with Regression Structure
49(12)
5.1 Optimal Prediction Under a Proportional Relationship
49(3)
5.2 Optimal Prediction Under a Linear Relationship
52(1)
5.3 Sample Design and Inference Under the Ratio Population Model
53(2)
5.4 Sample Design and Inference Under the Linear Population Model
55(1)
5.5 Combining Regression and Stratification
56(5)
6 Clustered Populations
61(11)
6.1 Sampling from a Clustered Population
62(1)
6.2 Optimal Prediction for a Clustered Population
63(3)
6.3 Optimal Design for Fixed Sample Size
66(2)
6.4 Optimal Design for Fixed Cost
68(2)
6.5 Optimal Design for Fixed Cost including Listing
70(2)
7 The General Linear Population Model
72(13)
7.1 A General Linear Model for a Population
72(2)
7.2 The Correlated General Linear Model
74(2)
7.3 Special Cases of the General Linear Population Model
76(3)
7.4 Model Choice
79(1)
7.5 Optimal Sample Design
80(1)
7.6 Derivation of BLUP Weights
81(4)
Part II Robust Model-Based Survey Methods
8 Robust Prediction Under Model Misspecification
85(16)
8.1 Robustness and the Homogeneous Population Model
85(3)
8.2 Robustness and the Ratio Population Model
88(5)
8.3 Robustness and the Clustered Population Model
93(2)
8.4 Non-parametric Prediction
95(6)
9 Robust Estimation of the Prediction Variance
101(7)
9.1 Robust Variance Estimation for the Ratio Estimator
101(2)
9.2 Robust Variance Estimation for General Linear Estimators
103(2)
9.3 The Ultimate Cluster Variance Estimator
105(3)
10 Outlier Robust Prediction
108(13)
10.1 Strategies for Outlier Robust Prediction
108(2)
10.2 Robust Parametric Bias Correction
110(3)
10.3 Robust Non-parametric Bias Correction
113(1)
10.4 Outlier Robust Design
114(1)
10.5 Outlier Robust Ratio Estimation: Some Empirical Evidence
115(2)
10.6 Practical Problems with Outlier Robust Estimators
117(4)
Part III Applications Of Model-Based Survey Inference
11 Inference for Non-linear Population Parameters
121(8)
11.1 Differentiable Functions of Population Means
121(2)
11.2 Solutions of Estimating Equations
123(2)
11.3 Population Medians
125(4)
12 Survey Inference via Sub-Sampling
129(10)
12.1 Variance Estimation via Independent Sub-Samples
130(1)
12.2 Variance Estimation via Dependent Sub-Samples
131(4)
12.3 Variance and Interval Estimation via Bootstrapping
135(4)
13 Estimation for Multipurpose Surveys
139(17)
13.1 Calibrated Weighting via Linear Unbiased Weighting
140(1)
13.2 Calibration of Non-parametric Weights
141(2)
13.3 Problems Associated With Calibrated Weights
143(2)
13.4 A Simulation Analysis of Calibrated and Ridged Weighting
145(6)
13.5 The Interaction Between Sample Weighting and Sample Design
151(5)
14 Inference for Domains
156(5)
14.1 Unknown Domain Membership
156(2)
14.2 Using Information about Domain Membership
158(1)
14.3 The Weighted Domain Estimator
159(2)
15 Prediction for Small Areas
161(34)
15.1 Synthetic Methods
162(2)
15.2 Methods Based on Random Area Effects
164(5)
15.3 Estimation of the Prediction MSE of the EBLUP
169(4)
15.4 Direct Prediction for Small Areas
173(4)
15.5 Estimation of Conditional MSE for Small Area Predictors
177(3)
15.6 Simulation-Based Comparison of EBLUP and MBD Prediction
180(4)
15.7 Generalised Linear Mixed Models in Small Area Prediction
184(1)
15.8 Prediction of Small Area Unemployment
185(7)
15.9 Concluding Remarks
192(3)
16 Model-Based Inference for Distributions and Quantiles
195(19)
16.1 Distribution Inference for a Homogeneous Population
195(2)
16.2 Extension to a Stratified Population
197(1)
16.3 Distribution Function Estimation under a Linear Regression Model
198(3)
16.4 Use of Non-parametric Regression Methods for Distribution Function Estimation
201(3)
16.5 Imputation vs. Prediction for a Wages Distribution
204(5)
16.6 Distribution Inference for Clustered Populations
209(5)
17 Using Transformations in Sample Survey Inference
214(19)
17.1 Back Transformation Prediction
211(4)
17.2 Model Calibration Prediction
215(3)
17.3 Smearing Prediction
218(1)
17.4 Outlier Robust Model Calibration and Smearing
219(2)
17.5 Empirical Results I
221(4)
17.6 Robustness to Model Misspecification
225(2)
17.7 Empirical Results II
227(2)
17.8 Efficient Sampling under Transformation and Balanced Weighting
229(4)
Bibliography 233(8)
Exercises 241(20)
Index 261
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