Sampling Theory and Practice (ICSA Book Series in Statistics)

✍ Scribed by Changbao Wu, Mary E. Thompson

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 371
• Category: Library

✦ Synopsis

The three parts of this book on survey methodology combine an introduction to basic sampling theory, engaging presentation of topics that reflect current research trends, and informed discussion of the problems commonly encountered in survey practice. These related aspects of survey methodology rarely appear together under a single connected roof, making this book a unique combination of materials for teaching, research and practice in survey sampling. Basic knowledge of probability theory and statistical inference is assumed, but no prior exposure to survey sampling is required. The first part focuses on the design-based approach to finite population sampling. It contains a rigorous coverage of basic sampling designs, related estimation theory, model-based prediction approach, and model-assisted estimation methods. The second part stems from original research conducted by the authors as well as important methodological advances in the field during the past threedecades. Topics include calibration weighting methods, regression analysis and survey weighted estimating equation (EE) theory, longitudinal surveys and generalized estimating equations (GEE) analysis, variance estimation and resampling techniques, empirical likelihood methods for complex surveys, handling missing data and non-response, and Bayesian inference for survey data. The third part provides guidance and tools on practical aspects of large-scale surveys, such as training and quality control, frame construction, choices of survey designs, strategies for reducing non-response, and weight calculation. These procedures are illustrated through real-world surveys. Several specialized topics are also discussed in detail, including household surveys, telephone and web surveys, natural resource inventory surveys, adaptive and network surveys, dual-frame and multiple frame surveys, and analysis of non-probability survey samples. This book is a self-contained introduction to survey sampling that provides a strong theoretical base with coverage of current research trends and pragmatic guidance and tools for conducting surveys.

✦ Table of Contents

Foreword
Preface
Contents
Acronyms
Part I Basic Concepts and Methods in Survey Sampling
1 Basic Concepts in Survey Sampling
1.1 Survey Populations
1.1.1 Eligibility Criteria for Survey Populations
1.1.2 Three Versions of Survey Populations
1.2 Survey Samples
1.2.1 Non-probability Survey Samples
1.2.2 Justifications for Using Survey Samples
1.3 Population Structures and Sampling Frames
1.3.1 Stratification
1.3.2 Clustering
1.3.3 Sampling Frames
1.4 Descriptive Population Parameters
1.5 Probability Sampling and Design-Based Inference
1.5.1 Probability Sampling Designs
1.5.2 Design-Based Inference in Survey Sampling
1.5.3 Principal Steps in Survey Sampling
1.6 Problems
2 Simple Single-Stage Sampling Methods
2.1 Simple Random Sampling Without Replacement
2.2 Simple Random Sampling with Replacement
2.3 Simple Systematic Sampling
2.4 Central Limit Theorems and Confidence Intervals
2.5 Sample Size Calculation
2.5.1 Accuracy Specified by the Absolute Tolerable Error
2.5.2 Accuracy Specified by the Relative Tolerable Error
2.6 Problems
3 Stratified Sampling and Cluster Sampling
3.1 Stratified Simple Random Sampling
3.1.1 Population Parameters
3.1.2 Sample Data
3.1.3 Estimation of the Overall Population Mean μy
3.1.4 Confidence Intervals
3.1.5 Justifications for Using Stratified Sampling
3.2 Sample Size Allocation Under Stratified Sampling
3.2.1 Proportional Allocation
3.2.2 Neyman Allocation
3.2.3 Optimal Allocation with Pre-specified Costor Variance
3.3 Single-Stage Cluster Sampling
3.3.1 Notation for Cluster Sampling
3.3.2 Single-Stage Cluster Sampling with Clusters Selected by SRSWOR
3.3.3 Estimation of the Population Total Ty
3.3.4 Estimation of the Population Mean μy
3.3.5 A Comparison Between SRSWOR and ClusterSampling
3.4 Two-Stage Cluster Sampling
3.4.1 Two-Stage Cluster Sampling with SRSWOR at Both Stages
3.4.2 Estimation of the Population Total Ty
3.4.3 Estimation of the Population Mean μy
3.5 Stratified Two-Stage Cluster Sampling
3.6 Problems
4 General Theory and Methods of Unequal Probability Sampling
4.1 Sample Inclusion Probabilities
4.2 The Horvitz-Thompson Estimator
4.2.1 The Yates-Grundy-Sen Variance Formula for the HT Estimator
4.2.2 The Hájek Variance Estimator
4.2.3 Estimation of the Population Mean μy and the Hájek Estimator
4.2.4 Estimation of the Population Distribution Function and Quantiles
4.3 PPS Sampling and the HT Estimator: An Optimal Strategy
4.3.1 PPS Sampling Designs
4.3.2 An Optimal Strategy
4.3.3 Basu's Elephant Example
4.4 PPS Sampling Procedures
4.4.1 PPS Sampling with n=2
4.4.2 The Randomized Systematic PPS Sampling Method
4.4.3 The Rao-Sampford Method
4.4.4 The Rao-Hartley-Cochran Method
4.5 PPS Sampling with Replacement
4.6 Poisson Sampling
4.7 Problems
5 Model-Based Prediction and Model-Assisted Estimation
5.1 Model-Based Prediction Methods
5.1.1 Model-Unbiased Prediction Estimator for μy
5.1.2 Variance Estimation for Model-Based Prediction
5.2 Model-Assisted Estimation Methods
5.2.1 The Simple Ratio Estimator
5.2.2 The Simple Regression Estimator
5.3 The Generalized Ratio Estimator
5.4 The Generalized Regression Estimator
5.4.1 GREG Under SRSWOR
5.4.2 GREG Under a General Sampling Design
5.4.3 The Generalized Difference Estimator
5.5 Problems
Part II Advanced Topics on Analysis of Probability Survey Samples
6 Calibration Weighting and Estimation
6.1 Calibration Estimators
6.1.1 Definition of Calibration Estimators
6.1.2 CalibrationEstimatorsUnder theChi-SquareDistance
6.2 Calibration Weighting
6.2.1 Generalized Exponential Tilting
6.2.2 Generalized Pseudo Empirical Likelihood
6.2.3 Comparisons Among Three Calibration Methods
6.2.4 Range-Restricted Calibration
6.3 Model-Calibration Estimators
6.3.1 Model-Calibration Estimators of the Population Total
6.3.2 Model-Calibration Estimators of Other Parameters
6.4 Raking Ratio Estimation
6.5 Additional Remarks
6.6 Problems
7 Regression Analysis and Estimating Equations
7.1 Parameters of Superpopulations and Survey Populations
7.1.1 Model Parameters and Estimating Functions
7.1.2 Survey Population Parameters
7.2 Survey Weighted Estimating Equations
7.2.1 Point Estimators
7.2.2 Design-Based Variance Estimation
7.2.3 Confidence Intervals and Regions
7.3 Regression Analysis with Survey Data
7.3.1 Linear Regression Analysis
7.3.2 Logistic Regression Analysis
7.4 Longitudinal Surveys and Generalized Estimating Equations
7.5 Problems
8 Empirical Likelihood Methods
8.1 Pseudo Empirical Likelihood and Sample EmpiricalLikelihood
8.2 Pseudo Empirical Likelihood for Non-stratified Sampling
8.2.1 Pseudo EL Without Auxiliary Information
8.2.2 Pseudo EL with Auxiliary Information
8.2.3 Examples of Pseudo EL Ratio Confidence Intervals
8.3 Pseudo Empirical Likelihood for Stratified Sampling
8.4 Computational Procedures
8.4.1 Constrained Maximization for Non-stratified Samples
8.4.2 Constrained Maximization for Stratified Samples
8.4.3 Profile Pseudo EL Ratio Confidence Intervals
8.5 Generalized Pseudo Empirical Likelihood
8.6 Pseudo Empirical Likelihood and Estimating Equations
8.6.1 General Results on Point and Variance Estimation
8.6.2 General Results on Hypothesis Tests
8.7 Sample Empirical Likelihood and Estimating Equations
8.7.1 General Results on Point and Variance Estimation
8.7.2 General Results on Hypothesis Tests
8.8 Design-Based Variable Selection Methods
8.8.1 Penalized Pseudo Empirical Likelihood
8.8.2 Penalized Sample Empirical Likelihood
8.9 Problems
9 Methods for Handling Missing Data
9.1 Issues with Missing Survey Data
9.1.1 Missing Data Mechanisms
9.1.2 Frameworks for Statistical Inference
9.1.3 Validity and Efficiency
9.2 Methods for Handling Unit Nonresponse
9.3 Methods for Handling Item Nonresponse
9.3.1 Complete-Case Analysis
9.3.2 Propensity Score Adjusted Analysis
9.3.3 Analysis with Imputation for Missing Values
9.3.4 Doubly Robust Estimation
9.4 Imputation for Missing Values
9.4.1 Single Imputation
9.4.2 Multiple Imputation
9.4.3 Fractional Imputation
9.5 Estimation with Missing Survey Data
9.5.1 Estimation of the Population Mean
9.5.2 Regression Analysis: Scenario I
9.5.3 Regression Analysis: Scenario II
9.6 Variance Estimation
9.6.1 PSA Estimators
9.6.2 Single Imputation Based Estimators
9.6.3 Multiple Imputation Estimators
9.7 Some Additional Notes on Missing Data Problems
9.8 Problems
10 Resampling and Replication Methods
10.1 The With-Replacement Bootstrap
10.1.1 Single-Stage Sampling
10.1.2 Stratified Sampling
10.1.3 Multi-Stage Cluster Sampling
10.2 The Pseudo-Population Bootstrap
10.3 The Multiplier Bootstrap
10.3.1 The Multiplier Bootstrap with Estimating Functions
10.3.2 Variance Estimation in the Presence of Nuisance Functionals
10.4 Replication Weights for Public-Use Survey Data
10.5 An Algebraic Construction of Replication Weights
10.6 Bootstrap Methods for Imputed Survey Data
10.7 Additional Remarks
10.8 Problems
11 Bayesian Empirical Likelihood Methods
11.1 Bayesian Inference with Survey Data
11.2 Bayesian Inference Based on Pseudo Empirical Likelihood
11.3 Bayesian Inference Based on Profile Pseudo EmpiricalLikelihood
11.4 Bayesian Inference for General Parameters
11.4.1 Bayesian Inference with a Fixed Prior
11.4.2 Bayesian Inference with an n-Dependent Prior
11.4.3 Computational Procedures
11.5 Additional Remarks
11.6 Problems
Part III Practical Issues and Special Topics in Survey Sampling
12 Area Frame Household Surveys
12.1 Household Surveys
12.2 The ITC China Survey Design
12.2.1 The Target Population and Method for DataCollection
12.2.2 Sample Size Determination
12.2.3 Frame Construction and Sample Selection
12.2.4 Survey Measures and Questionnaire Development
12.3 The ITC China Survey Procedures
12.3.1 Survey Team
12.3.2 Training
12.3.3 Quality Control
12.3.4 Measures of Data Quality
12.4 Weight Calculation
12.4.1 Dealing with Cluster Level Unit Nonresponse
12.4.2 Cross-Sectional Weights
12.4.3 Longitudinal Weights
12.5 Additional Remarks
13 Telephone and Web Surveys
13.1 Telephone Survey Frames and Sampling Methods
13.2 Components of Survey Error for Telephone Surveys
13.3 Web Survey Frames and Sampling Methods
13.4 Mixed Mode Surveys
13.5 Construction of Survey Weights
13.5.1 Survey Weights for RDD Surveys
13.5.2 Survey Weights for Web Surveys
13.6 Problems
14 Natural Resource Inventory Surveys
14.1 Surveys of Non-human Populations
14.1.1 Non-human Population Surveys
14.1.2 Features of Natural Resource Inventory Surveys
14.2 Fish Abundance Surveys
14.2.1 The Fish Abundance Index
14.2.2 The FPI Survey Design
14.3 Estimation of Fish Abundance Indices
14.3.1 Models for the Catching Process
14.3.2 Point Estimation
14.3.3 Variance Estimation
14.3.4 Pseudo Empirical Likelihood Methods
15 Adaptive and Network Surveys
15.1 Finite Populations with Network Structure
15.1.1 Terminology and Notation
15.1.2 Estimation Problems
15.1.3 Probability Models for Networks
15.2 Link Tracing Sampling Designs
15.2.1 Snowball Sampling
15.2.2 Respondent Driven Sampling
15.2.3 Indirect Sampling
15.2.4 Adaptive Cluster Sampling
15.3 Problem
16 Dual Frame and Multiple Frame Surveys
16.1 Estimation with Dual Frame Surveys
16.2 Pseudo Empirical Likelihood for Dual Frame Surveys
16.2.1 Point Estimation
16.2.2 Confidence Intervals
16.2.3 Auxiliary Information and Computational Procedures
16.3 A Multiplicity-Based Approach for Multiple Frame Surveys
16.3.1 The Single-Frame Multiplicity-Based Estimator
16.3.2 Multiplicity-Based Pseudo Empirical Likelihood Approach
16.4 A Bootstrap Procedure for Multiple Frame Surveys
16.5 Additional Remarks
17 Non-probability Survey Samples
17.1 Non-probability Samples
17.2 General Setting and Basic Assumptions
17.3 Sample Matching and Mass Imputation
17.4 Estimation of Propensity Scores
17.5 Estimation of the Population Mean
17.6 Variance Estimation
17.7 An Example and Additional Remarks
A R Code for PPS Sampling, Empirical Likelihood and Regression Analysis
A.1 Randomized Systematic PPS Sampling
A.2 Rao-Sampford PPS Sampling
A.2.1 Select a PPS Sample
A.2.2 Compute Second Order Inclusion Probabilities
A.3 Empirical Likelihood Methods
A.3.1 Lagrange Multiplier: Univariate Case
A.3.2 Lagrange Multiplier: Vector Case
A.3.3 Lagrange Multiplier: Stratified Sampling
A.3.4 Empirical Likelihood Ratio Confidence Intervals
A.4 Survey Weighted Regression Analysis
A.4.1 Linear Regression Analysis
A.4.2 Logistic Regression Analysis
References
Author Index
Subject Index