Finite population sampling and inference : a prediction approach /
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Author / Creator: | Valliant, Richard, 1950- |
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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 |
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