Finite population sampling and inference : a prediction approach /

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Bibliographic Details
Author / Creator:Valliant, Richard, 1950-
Imprint:New York : John Wiley, c2000.
Description:xvii, 504 p. : ill. ; 24 cm.
Language:English
Series:Wiley series in probability and statistics. Survey methodology section
Subject:Sampling (Statistics)
Prediction theory.
Prediction theory.
Sampling (Statistics)
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/4338348
Hidden Bibliographic Details
Other authors / contributors:Dorfman, Alan H.
Royall, Richard M.
ISBN:0471293415 (cloth : alk. paper)
Notes:Includes bibliographical references and index.
Table of Contents:
  • Preface
  • 1.. Introduction to Prediction Theory
  • 1.1. Sampling Theory and the Rest of Statistics
  • 1.2. Prediction Theory
  • 1.3. Probability Sampling Theory
  • 1.3.1. Techniques Used in Probability Sampling
  • 1.3.2. Some Mathematical Details
  • 1.4. Which Approach to Use?
  • 1.5. Why Use Random Sampling?
  • Exercises
  • 2.. Prediction Theory Under the General Linear Model
  • 2.1. Definitions and a Simple Example
  • 2.2. General Prediction Theorem
  • 2.3. BLU Predictor Under Some Simple Models
  • 2.4. Unit Weights
  • 2.5. Asymptotic Normality of the BLU Predictor
  • 2.6. Ignorable and Nonignorable Sample Selection Methods
  • 2.6.1. Examples
  • 2.6.2. Formal Definition of Ignorable Selection
  • 2.7. Comparisons with Design-Based Regression Estimation
  • Exercises
  • 3.. Bias-Robustness
  • 3.1. Design and Bias
  • 3.2. Polynomial Framework and Balanced Samples
  • 3.2.1. Expansion Estimator and Balanced Samples
  • 3.2.2. Order of the Bias of the Expansion Estimator
  • 3.2.3. Ratio Estimator and Balanced Samples
  • 3.2.4. Bias-Robust Strategies
  • 3.2.5. Simulation Study to Illustrate Conditional Biases and Mean Squared Errors
  • 3.2.6. Balance and Multiple Y Variables
  • 3.3. Weighted Balance
  • 3.3.1. Elementary Estimators Unbiased Under Weighted Balance
  • 3.3.2. BLU Estimators and Weighted Balance
  • 3.4. Methods of Selecting Balanced Samples
  • 3.4.1. Simple Random Sampling
  • 3.4.2. Systematic Equal Probability Sampling
  • 3.4.3. Stratification Based on the Auxiliary
  • 3.4.4. Restricted Random Sampling
  • 3.4.5. Sampling for Weighted Balance
  • 3.4.6. Restricted pps Sampling
  • 3.4.7. Partial Balancing
  • 3.5. Simulation Study of Weighted Balance
  • 3.5.1. Results Using the Hospitals Population
  • 3.5.2. Interaction of Model Specification with Sample Configuration
  • 3.6. Summary
  • 3.7. Robustness and Design-Based Inference
  • Exercises
  • 4.. Robustness and Efficiency
  • 4.1. Introduction
  • 4.2. General Linear Model
  • 4.2.1. BLU Predictor Under the General Linear Model with Diagonal Variance Matrix
  • 4.2.2. Examples of Minimal Models
  • 4.3. Comparisons Using an Artificial Population
  • 4.3.1. Results for Probability Proportional to x Sampling and x-Balance
  • 4.3.2. Results for Probability Proportional to x[superscript 1/2] Sampling and x[superscript 1/2]-Balance
  • 4.3.3. Results for Equal Probability Systematic Sampling and Simple Balance
  • 4.4. Sample Size Determination
  • 4.5. Summary and Perspective
  • 4.6. Remarks on Design-Based Inference
  • Exercises
  • 5.. Variance Estimation
  • 5.1. Examples of Robust Variance Estimation
  • 5.1.1. Homoscedastic Through the Origin Model
  • 5.1.2. Variance Estimators for the Ratio Estimator
  • 5.2. Variance Estimation of a Linear Function of the Parameter
  • 5.3. Sandwich Estimator of Variance
  • 5.3.1. Consistency of v[subscript R]
  • 5.3.2. Some Comments on the Requirements for Consistency of the Sandwich Estimator
  • 5.4. Variants on the Basic Robust Variance Estimator
  • 5.4.1. Internal and External Adjustments to the Sandwich Estimator
  • 5.4.2. Jackknife Variance Estimator
  • 5.5. Variance Estimation for Totals
  • 5.5.1. Some Simple Examples
  • 5.5.2. Effect of a Large Sampling Fraction
  • 5.6. Misspecification of the Regression Component
  • 5.7. Hidden Regression Components
  • 5.7.1. Some Artificial Examples
  • 5.7.2. Counties 70 Population
  • 5.7.3. Lurking Discrete Skewed Variables
  • 5.8. Comparisons with Design-Based Variance Estimation
  • Exercises
  • 6.. Stratified Populations
  • 6.1. Stratification with Homogeneous Subpopulations
  • 6.2. Stratified Linear Model and Weighted Balanced Samples
  • 6.2.1. Optimal Allocation for Stratified Balanced Sampling
  • 6.2.2. Case of a Single Model for the Population
  • 6.2.3. Case of a Single Auxiliary Variable
  • 6.3. Sampling Fractions Greater Than 1
  • 6.4. Allocation to Strata in More Complicated Cases
  • 6.4.1. Contrasts Between Strata
  • 6.4.2. More Than One Target Variable
  • 6.5. Two Traditional Topics
  • 6.5.1. Efficiency of the Separate Ratio Estimator
  • 6.5.2. Formation of Strata
  • 6.6. Some Empirical Results on Strata Formation
  • 6.7. Variance Estimation in Stratified Populations
  • 6.8. Stratification in Design-Based Theory
  • Exercises
  • 7.. Models with Qualitative Auxiliaries
  • 7.1. Simple Example
  • 7.2. Factors, Levels, and Effects
  • 7.3. Generalized Inverses
  • 7.4. Estimating Linear Combinations of the Y's
  • 7.5. One-Way Classification
  • 7.6. Two-Way Nested Classification
  • 7.7. Two-Way Classification Without Interaction
  • 7.8. Two-Way Classification With Interaction
  • 7.9. Combining Qualitative and Quantitative Auxiliaries
  • 7.9.1. General Covariance Model
  • 7.9.2. One-Way Classification with a Single Covariate
  • 7.9.3. Examples
  • 7.10. Variance Estimation
  • 7.10.1. Basic Robust Alternatives
  • 7.10.2. Jackknife Variance Estimator
  • Exercises
  • 8.. Clustered Populations
  • 8.1. Intracluster Correlation Model for a Clustered Population
  • 8.1.1. Discussion of the Common Mean Model
  • 8.1.2. Simple Sample Designs
  • 8.2. Class of Unbiased Estimators Under the Common Mean Model
  • 8.2.1. One-Stage Cluster Sampling
  • 8.2.2. BLU Predictor
  • 8.2.3. Variance Component Model
  • 8.3. Estimation of Parameters in the Constant Parameter Model
  • 8.3.1. ANOVA Estimators
  • 8.3.2. Maximum Likelihood Estimators
  • 8.3.3. Lower Bound on the Intracluster Correlation
  • 8.4. Simulation Study for the Common Mean Model
  • 8.5. Biases of Common Mean Estimators Under a More General Model
  • 8.6. Estimation Under a More General Regression Model
  • 8.7. Robustness and Optimality
  • 8.8. Efficient Design for the Common Mean Model
  • 8.8.1. Choosing the Set of Sample Clusters for the BLU Estimator
  • 8.8.2. Choosing the Set of Sample Clusters for the Unbiased Estimators
  • 8.8.3. Optimal Allocation of Second-Stage Units Given a Fixed Set of First-Stage Sample Units
  • 8.8.4. Optimal First and Second-Stage Allocation Considering Costs
  • 8.9. Estimation When Cluster Sizes Are Unknown
  • 8.10. Two-Stage Sampling in Design-Based Practice
  • Exercises
  • 9.. Robust Variance Estimation in Two-Stage Cluster Sampling
  • 9.1. Common Mean Model and a General Class of Variance Estimators
  • 9.2. Other Variance Estimators
  • 9.2.1. Non-Robust ANOVA Estimator
  • 9.2.2. Alternative Robust Variance Estimators
  • 9.3. Examples of the Variance Estimators
  • 9.3.1. Ratio Estimator
  • 9.3.2. Mean of Ratios Estimator
  • 9.3.3. Numerical Illustrations
  • 9.4. Variance Estimation for an Estimated Total--Unknown Cluster Sizes
  • 9.5. Regression Estimator
  • 9.5.1. Sandwich Variance Estimator
  • 9.5.2. Adjustments to the Sandwich Estimator
  • 9.5.3. Jackknife Estimator
  • 9.6. Comparisons of Variance Estimators in a Simulation Study
  • Exercises
  • 10.. Alternative Variance Estimation Methods
  • 10.1. Estimating the Variance of Estimators of Nonlinear Functions
  • 10.1.1. Variance Estimation for a Ratio of Estimated Totals
  • 10.1.2. Jackknife and Nonlinear Functions
  • 10.2. Balanced Half-Sample Variance Estimation
  • 10.2.1. Application to the Stratified Expansion Estimator
  • 10.2.2. Orthogonal Arrays
  • 10.2.3. Extension to Nonlinear Functions
  • 10.2.4. Two-Stage Sampling
  • 10.2.5. Other Forms of the BHS Variance Estimator
  • 10.2.6. Partially Balanced Half-Sampling
  • 10.2.7. Design-based Properties
  • 10.3. Generalized Variance Functions
  • 10.3.1. Some Theory for GVF's
  • 10.3.2. Estimation of GVF Parameters
  • Exercises
  • 11.. Special Topics and Open Questions
  • 11.1. Estimation in the Presence of Outliers
  • 11.1.1. Gross Error Model
  • 11.1.2. Simple Regression Model
  • 11.1.3. Areas for Research
  • 11.2. Nonlinear Models
  • 11.2.1. Model for Bernoulli Random Variables
  • 11.2.2. Areas for Research
  • 11.3. Nonparametric Estimation of Totals
  • 11.3.1. Nonparametric Regression for Totals
  • 11.3.2. Nonparametric Calibration Estimation
  • 11.4. Distribution Function and Quantile Estimation
  • 11.4.1. Estimation Under Homogeneous and Stratified Models
  • 11.4.2. Estimation of F[subscript N](.) Under a Regression Model
  • 11.4.3. Large Sample Properties
  • 11.4.4. The Effect of Model Misspecification
  • 11.4.5. Design-Based Approaches
  • 11.4.6. Nonparametric Regression-Based Estimators
  • 11.4.7. Some Open Questions
  • 11.5. Small Area Estimation
  • 11.5.1. Estimation When Cell Means Are Unrelated
  • 11.5.2. Cell Means Determined by Class but Uncorrelated
  • 11.5.3. Synthetic and Composite Estimators
  • 11.5.4. Using Auxiliary Data
  • 11.5.5. Auxiliary Data at the Cell Level
  • 11.5.6. Need for a Small Area Estimation Canon
  • Exercises
  • Appendix A.. Some Basic Tools
  • A.1. Orders of Magnitude, O(.) and o(.)
  • A.2. Convergence in Probability and in Distribution
  • A.3. Probabilistic Orders of Magnitude, O[subscript p](.) and o[subscript p](.)
  • A.4. Chebyshev's Inequality
  • A.5. Cauchy-Schwarz Inequality
  • A.6. Slutsky's Theorem
  • A.7. Taylor's Theorem
  • A.7.1. Univariate Version
  • A.7.2. Multivariate Version
  • A.8. Central Limit Theorems for Independent, not Identically Distributed Random Variables
  • A.9. Central Limit Theorem for Simple Random Sampling
  • A.10. Generalized Inverse of a Matrix
  • Appendix B.. Datasets
  • B.1. Cancer Population
  • B.2. Hospitals Population
  • B.3. Counties 60 Population
  • B.4. Counties 70 Population
  • B.5. Labor Force Population
  • B.6. Third Grade Population
  • Appendix C.. S-PLUS Functions
  • Bibliography
  • Answers to Select Exercises
  • Author Index
  • Subject Index