Finite Population Sampling and Inference A Prediction Approach

by Valliant, Richard; Dorfman, Alan H.; Royall, Richard M.

• ISBN13: 9780471293415
• ISBN10: 0471293415
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-09-08
• Publisher: Wiley-Interscience

Summary

* Over 260 references to finite population sampling, linear models, and other relevant literature

Author Biography

RICHARD VALLIANT, PhD, is Associate Director at Westat, Rockville, Maryland. <BR>

Table of Contents

Preface	xv
Introduction to Prediction Theory	1	(24)
Sampling Theory and the Rest of Statistics	1	(1)
Prediction Theory	2	(5)
Probability Sampling Theory	7	(7)
Techniques Used in Probability Sampling	9	(2)
Some Mathematical Details	11	(3)
Which Approach to Use?	14	(5)
Why Use Random Sampling?	19	(6)
Exercises	22	(3)
Prediction Theory Under the General Linear Model	25	(24)
Definitions and a Simple Example	26	(3)
General Prediction Theorem	29	(2)
BLU Predictor Under Some Simple Models	31	(1)
Unit Weights	32	(2)
Asymptotic Normality of the BLU Predictor	34	(1)
Ignorable and Nonignorable Sample Selection Methods	35	(5)
Examples	36	(1)
Formal Definition of Ignorable Selection	36	(4)
Comparisons with Design-Based Regression Estimation	40	(9)
Exercises	44	(5)
Bias-Robustness	49	(46)
Design and Bias	50	(3)
Polynomial Framework and Balanced Samples	53	(8)
Expansion Estimator and Balanced Samples	54	(1)
Order of the Bias of the Expansion Estimator	55	(1)
Ratio Estimator and Balanced Samples	55	(1)
Bias-Robust Strategies	56	(1)
Simulation Study to Illustrate Conditional Biases and Mean Squared Errors	57	(2)
Balance and Multiple Y Variables	59	(2)
Weighted Balance	61	(4)
Elementary Estimators Unbiased Under Weighted Balance	62	(1)
BLU Estimators and Weighted Balance	63	(2)
Methods of Selecting Balanced Samples	65	(12)
Simple Random Sampling	66	(1)
Systematic Equal Probability Sampling	67	(1)
Stratification Based on the Auxiliary	68	(3)
Restricted Random Sampling	71	(1)
Sampling for Weighted Balance	72	(2)
Restricted pps Sampling	74	(3)
Partial Balancing	77	(1)
Simulation Study of Weighted Balance	77	(8)
Results Using the Hospitals Population	78	(4)
Interaction of Model Specification with Sample Configuration	82	(3)
Summary	85	(1)
Robustness and Design-Based Inference	85	(10)
Exercises	90	(5)
Robustness and Efficiency	95	(30)
Introduction	95	(1)
General Linear Model	96	(7)
BLU Predictor Under the General Linear Model with Diagonal Variance Matrix	97	(4)
Examples of Minimal Models	101	(2)
Comparisons Using an Artificial Population	103	(11)
Results for Probability Proportional to x Sampling and x-Balance	105	(2)
Results for Probability Proportional to x1/2 Sampling and x1/2-Balance	107	(3)
Results for Equal Probability Systematic Sampling and Simple Balance	110	(4)
Sample Size Determination	114	(4)
Summary and Perspective	118	(1)
Remarks on Design-Based Inference	119	(6)
Exercises	122	(3)
Variance Estimation	125	(42)
Examples of Robust Variance Estimation	127	(7)
Homoscedastic Through the Origin Model	127	(3)
Variance Estimators for the Ratio Estimator	130	(4)
Variance Estimation of a Linear Function of the Parameter	134	(1)
Sandwich Estimator of Variance	135	(4)
Consistency of vR	136	(2)
Some Comments on the Requirements for Consistency of the Sandwich Estimator	138	(1)
Variants on the Basic Robust Variance Estimator	139	(5)
Internal and External Adjustments to the Sandwich Estimator	139	(2)
Jackknife Variance Estimator	141	(3)
Variance Estimation for Totals	144	(5)
Some Simple Examples	146	(3)
Effect of a Large Sampling Fraction	149	(1)
Misspecification of the Regression Component	149	(3)
Hidden Regression Components	152	(9)
Some Artificial Examples	153	(4)
Counties 70 Population	157	(4)
Lurking Discrete Skewed Variables	161	(1)
Comparisons with Design-Based Variance Estimation	161	(6)
Exercises	164	(3)
Stratified Populations	167	(44)
Stratification with Homogeneous Subpopulations	168	(5)
Stratified Linear Model and Weighted Balanced Samples	173	(6)
Optimal Allocation for Stratified Balanced Sampling	174	(1)
Case of a Single Model for the Population	175	(2)
Case of a Single Auxiliary Variable	177	(2)
Sampling Fractions Greater Than 1	179	(2)
Allocation to Strata in More Complicated Cases	181	(5)
Contrasts Between Strata	182	(2)
More Than One Target Variable	184	(2)
Two Traditional Topics	186	(6)
Efficiency of the Separate Ratio Estimator	186	(3)
Formation of Strata	189	(3)
Some Empirical Results on Strata Formation	192	(5)
Variance Estimation in Stratified Populations	197	(3)
Stratification in Design-Based Theory	200	(11)
Exercises	205	(6)
Models with Qualitative Auxiliaries	211	(35)
Simple Example	211	(2)
Factors, Levels, and Effects	213	(1)
Generalized Inverses	214	(3)
Estimating Linear Combinations of the Y's	217	(3)
One-Way Classification	220	(3)
Two-Way Nested Classification	223	(2)
Two-Way Classification Without Interaction	225	(1)
Two-Way Classification With Interaction	226	(5)
Combining Qualitative and Quantitative Auxiliaries	231	(6)
General Covariance Model	232	(2)
One-Way Classification with a Single Covariate	234	(1)
Examples	235	(2)
Variance Estimation	237	(9)
Basic Robust Alternatives	238	(2)
Jackknife Variance Estimator	240	(2)
Exercises	242	(4)
Clustered Populations	246	(50)
Intracluster Correlation Model for a Clustered Population	247	(3)
Discussion of the Common Mean Model	248	(1)
Simple Sample Designs	249	(1)
Class of Unbiased Estimators Under the Common Mean Model	250	(7)
One-Stage Cluster Sampling	252	(2)
BLU Predictor	254	(2)
Variance Component Model	256	(1)
Estimation of Parameters in the Constant Parameter Model	257	(4)
ANOVA Estimators	257	(1)
Maximum Likelihood Estimators	258	(3)
Lower Bound on the Intracluster Correlation	261	(1)
Simulation Study for the Common Mean Model	261	(3)
Biases of Common Mean Estimators Under a More General Model	264	(2)
Estimation Under a More General Regression Model	266	(5)
Robustness and Optimality	271	(4)
Efficient Design for the Common Mean Model	275	(8)
Choosing the Set of Sample Clusters for the BLU Estimator	275	(1)
Choosing the Set of Sample Clusters for the Unbiased Estimators	276	(1)
Optimal Allocation of Second-Stage Units Given a Fixed Set of First-Stage Sample Units	277	(2)
Optimal First and Second-Stage Allocation Considering Costs	279	(4)
Estimation When Cluster Sizes Are Unknown	283	(4)
Two-Stage Sampling in Design-Based Practice	287	(9)
Exercises	290	(6)
Robust Variance Estimation in Two-Stage Cluster Sampling	296	(27)
Common Mean Model and a General Class of Variance Estimators	296	(3)
Other Variance Estimators	299	(6)
Non-Robust ANOVA Estimator	300	(1)
Alternative Robust Variance Estimators	301	(4)
Examples of the Variance Estimators	305	(4)
Ratio Estimator	305	(2)
Mean of Ratios Estimator	307	(1)
Numerical Illustrations	307	(2)
Variance Estimation for an Estimated Total---Unknown Cluster Sizes	309	(1)
Regression Estimator	310	(8)
Sandwich Variance Estimator	311	(2)
Adjustments to the Sandwich Estimator	313	(1)
Jackknife Estimator	314	(4)
Comparisons of Variance Estimators in a Simulation Study	318	(5)
Exercises	320	(3)
Alternative Variance Estimation Methods	323	(28)
Estimating the Variance of Estimators of Nonlinear Functions	323	(7)
Variance Estimation for a Ratio of Estimated Totals	326	(3)
Jackknife and Nonlinear Functions	329	(1)
Balanced Half-Sample Variance Estimation	330	(14)
Application to the Stratified Expansion Estimator	331	(2)
Orthogonal Arrays	333	(1)
Extension to Nonlinear Functions	334	(2)
Two-Stage Sampling	336	(4)
Other Forms of the BHS Variance Estimator	340	(1)
Partially Balanced Half-Sampling	341	(3)
Design-based Properties	344	(1)
Generalized Variance Functions	344	(7)
Some Theory for GVF's	345	(2)
Estimation of GVF Parameters	347	(1)
Exercises	348	(3)
Special Topics and Open Questions	351	(62)
Estimation in the Presence of Outliers	352	(15)
Gross Error Model	354	(7)
Simple Regression Model	361	(5)
Areas for Research	366	(1)
Nonlinear Models	367	(5)
Model for Bernoulli Random Variables	370	(2)
Areas for Research	372	(1)
Nonparametric Estimation of Totals	372	(5)
Nonparametric Regression for Totals	373	(2)
Nonparametric Calibration Estimation	375	(2)
Distribution Function and Quantile Estimation	377	(17)
Estimation Under Homogeneous and Stratified Models	380	(2)
Estimation of FN(·) Under a Regression Model	382	(5)
Large Sample Properties	387	(1)
The Effect of Model Misspecification	388	(2)
Design-Based Approaches	390	(1)
Nonparametric Regression-Based Estimators	391	(2)
Some Open Questions	393	(1)
Small Area Estimation	394	(19)
Estimation When Cell Means Are Unrelated	395	(1)
Cell Means Determined by Class but Uncorrelated	396	(4)
Synthetic and Composite Estimators	400	(2)
Using Auxiliary Data	402	(2)
Auxiliary Data at the Cell Level	404	(2)
Need for a Small Area Estimation Canon	406	(1)
Exercises	407	(6)
Appendix A. Some Basic Tools	413	(7)
A.1 Orders of Magnitude, O(·) and o(·)	413	(1)
A.2 Convergence in Probability and in Distribution	413	(1)
A.3 Probabilistic Orders of Magnitude, Op(·) and op(·)	414	(1)
A.4 Chebyshev's Inequality	414	(1)
A.5 Cauchy-Schwarz Inequality	414	(1)
A.6 Slutsky's Theorem	414	(1)
A.7 Taylor's Theorem	415	(1)
A.7.1 Univariate Version	415	(1)
A.7.2 Multivariate Version	415	(1)
A.8 Central Limit Theorems for Independent, not Identically Distributed Random Variables	415	(1)
A.9 Central Limit Theorem for Simple Random Sampling	416	(1)
A.10 Generalized Inverse of a Matrix	417	(3)
Appendix B. Datasets	420	(26)
B.1 Cancer Population	422	(2)
B.2 Hospitals Population	424	(4)
B.3 Counties 60 Population	428	(3)
B.4 Counties 70 Population	431	(3)
B.5 Labor Force Population	434	(10)
B.6 Third Grade Population	444	(2)
Appendix C. S-PLUS Functions	446	(14)
Bibliography	460	(14)
Answers to Select Exercises	474	(10)
Author Index	484	(4)
Subject Index	488