Chambers R., Clark R. An Introduction to Model-Based Survey Sampling with Applications

Oxford: Oxford University Press, 2012. — 265 p. — (Oxford Statistical Science Series). — ISBN: 978-0-19-856662-5.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 modeling and data analysis and includes exercises and solutions.Basics of Model-Based Survey Inference
Introduction
Why Sample?
Target Populations and Sampling FramesPopulation Models and Non-Informative Sampling
The Model-Based Approach
Optimal Prediction
Homogeneous Populations
Random Sampling Models
A Model for a Homogeneous Population
Empirical Best Prediction and Best Linear Unbiased Prediction of the Population Total
Variance Estimation and Confidence Intervals
Predicting the Value of a Linear Population Parameter
How Large a Sample?
Selecting a Simple Random Sample
A Generalisation of the Homogeneous Model
Stratified Populations
The Homogeneous Strata Population Model
Optimal Prediction Under Stratification
Stratified Sample Design
Proportional Allocation
Optimal Allocation
Allocation for Proportions
How Large a Sample?
Defining Stratum Boundaries
Model-Based Stratification
Equal Aggregate Size Stratification
Multivariate Stratification
How Many Strata?
Populations with Regression Structure
Optimal Prediction Under a Proportional Relationship
Optimal Prediction Under a Linear Relationship
Sample Design and Inference Under the Ratio Population Model
Sample Design and Inference Under the Linear Population Model
Combining Regression and Stratification
Clustered Populations
Sampling from a Clustered Population
Optimal Prediction for a Clustered Population
Optimal Design for Fixed Sample Size
Optimal Design for Fixed Cost
Optimal Design for Fixed Cost including Listing
The General Linear Population Model
A General Linear Model for a Population
The Correlated General Linear Model
Special Cases of the General Linear Population Model
Model Choice
Optimal Sample Design
Derivation of BLUP Weights
Robust Model-Based Survey Methods
Robust Prediction Under Model Misspecification
Robustness and the Homogeneous Population Model
Robustness and the Ratio Population Model
Robustness and the Clustered Population Model
Non-parametric Prediction
Robust Estimation of the Prediction Variance
Robust Variance Estimation for the Ratio Estimator
Robust Variance Estimation for General Linear Estimators
The Ultimate Cluster Variance Estimator
Outlier Robust Prediction
Strategies for Outlier Robust Prediction
Robust Parametric Bias Correction
Robust Non-parametric Bias Correction
Outlier Robust Design
Outlier Robust Ratio Estimation: Some Empirical Evidence
Practical Problems with Outlier Robust Estimators
Applications of Model-Based Survey Inference
Inference for Non-linear Population Parameters
Differentiable Functions of Population Means
Solutions of Estimating Equations
Population Medians
Survey Inference via Sub-Sampling
Variance Estimation via Independent Sub-Samples
Variance Estimation via Dependent Sub-Samples
Variance and Interval Estimation via Bootstrapping
Estimation for Multipurpose Surveys
Calibrated Weighting via Linear Unbiased Weighting
Calibration of Non-parametric Weights
Problems Associated With Calibrated Weights
A Simulation Analysis of Calibrated and Ridged Weighting
The Interaction Between Sample Weighting and Sample Design
Inference for Domains
Unknown Domain Membership
Using Information about Domain Membership
The Weighted Domain Estimator
Prediction for Small Areas
Synthetic Methods
Methods Based on Random Area Effects
Estimation of the Prediction MSE of the EBLUP
Direct Prediction for Small Areas
Estimation of Conditional MSE for Small Area Predictors
Simulation-Based Comparison of EBLUP and MBD Prediction
Generalised Linear Mixed Models in Small Area Prediction
Prediction of Small Area Unemployment
Concluding Remarks
Model-Based Inference for Distributions and Quantiles
Distribution Inference for a Homogeneous Population
Extension to a Stratified Population
Distribution Function Estimation under a Linear Regression Model
Use of Non-parametric Regression Methods for Distribution Function Estimation
Imputation vs. Prediction for a Wages Distribution
Distribution Inference for Clustered Populations
Using Transformations in Sample Survey Inference
Back Transformation Prediction
Model Calibration Prediction
Smearing Prediction
Outlier Robust Model Calibration and Smearing
Empirical Results I
Robustness to Model Misspecification
Empirical Results II
Efficient Sampling under Transformation and Balanced WeightingExercises