Finite Population Sampling and Inference A Prediction Approach

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

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ISBN: 9780471293415 | 0471293415
Cover: Hardcover
Copyright: 9/8/2000

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Summary

Author Biography

Supplemental Materials

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

Preface

Introduction to Prediction Theory

(24)

Sampling Theory and the Rest of Statistics

(1)

Prediction Theory

(5)

Probability Sampling Theory

(7)

Techniques Used in Probability Sampling

(2)

Some Mathematical Details

(3)

Which Approach to Use?

(5)

Why Use Random Sampling?

(6)

Exercises

(3)

Prediction Theory Under the General Linear Model

(24)

Definitions and a Simple Example

(3)

General Prediction Theorem

(2)

BLU Predictor Under Some Simple Models

(1)

Unit Weights

(2)

Asymptotic Normality of the BLU Predictor

(1)

Ignorable and Nonignorable Sample Selection Methods

(5)

Examples

(1)

Formal Definition of Ignorable Selection

(4)

Comparisons with Design-Based Regression Estimation

(9)

Exercises

(5)

Bias-Robustness

(46)

Design and Bias

(3)

Polynomial Framework and Balanced Samples

(8)

Expansion Estimator and Balanced Samples

(1)

Order of the Bias of the Expansion Estimator

(1)

Ratio Estimator and Balanced Samples

(1)

Bias-Robust Strategies

(1)

Simulation Study to Illustrate Conditional Biases and Mean Squared Errors

(2)

Balance and Multiple Y Variables

(2)

Weighted Balance

(4)

Elementary Estimators Unbiased Under Weighted Balance

(1)

BLU Estimators and Weighted Balance

(2)

Methods of Selecting Balanced Samples

(12)

Simple Random Sampling

(1)

Systematic Equal Probability Sampling

(1)

Stratification Based on the Auxiliary

(3)

Restricted Random Sampling

(1)

Sampling for Weighted Balance

(2)

Restricted pps Sampling

(3)

Partial Balancing

(1)

Simulation Study of Weighted Balance

(8)

Results Using the Hospitals Population

(4)

Interaction of Model Specification with Sample Configuration

(3)

Summary

(1)

Robustness and Design-Based Inference

(10)

Exercises

(5)

Robustness and Efficiency

(30)

Introduction

(1)

General Linear Model

(7)

BLU Predictor Under the General Linear Model with Diagonal Variance Matrix

(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

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Finite Population Sampling and Inference A Prediction Approach

Summary

Author Biography

Table of Contents

Supplemental Materials