Introduction to Variance Estimation
by Wolter, Kirk M.Edition: 2nd
Format: Hardcover
Pub. Date: 2007-02-23
Publisher(s): Springer Verlag
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Summary
We live in the information age. Statistical surveys are used every day to determine or evaluate public policy and to make important business decisions. Correct methods for computing the precision of the survey data and for making inferences to the target population are absolutely essential to sound decision making. Now in its second edition, Introduction to Variance Estimation has for more than twenty years provided the definitive account of the theory and methods for correct precision calculations and inference, including examples of modern, complex surveys in which the methods have been used successfully. The book provides instruction on the methods that are vital to data-driven decision making in business, government, and academe. It will appeal to survey statisticians and other scientists engaged in the planning and conduct of survey research, and to those analyzing survey data and charged with extracting compelling information from such data. It will appeal to graduate students and university faculty who are focused on the development of new theory and methods and on the evaluation of alternative methods. Software developers concerned with creating the computer tools necessary to enable sound decision-making will find it essential.Prerequisites include knowledge of the theory and methods of mathematical statistics and graduate coursework in survey statistics. Practical experience with real surveys is a plus and may be traded off against a portion of the requirement for graduate coursework.This second edition reflects shifts in the theory and practice of sample surveys that have occurred since the content of the first edition solidified in the early 1980's. Additional replication type methods appeared during this period and have featured prominently in journal publications. Reflecting these developments, the second edition now includes a new major chapter on the bootstrap method of variance estimation. This edition also includes extensive new material on Taylor series methods, especially as they apply to newer methods of analysis such as logistic regression or the generalized regression estimator. An introductory section on survey weighting has been added. Sections on Hadamard matrices and computer software have been substantially scaled back. Fresh material on these topics is now readily available on the Internet or from commercial sources.Kirk Wolter is a Senior Fellow at NORC, Director of the Center for Excellency in Survey Research, and Professor in the Department of Statistics, University of Chicago. He is a Fellow of the American Statistical Association and a Member of the International Statistical Institute. He is a past president of the International Association of Survey Statisticians and a past chair of the Survey Research Methods Section of the American Statistical Association. During the last 35 years, he has participated in the planning, execution, and analysis of large-scale complex surveys and has provided instruction in survey statistics both in America and around the world.
Author Biography
Kirk M. Wolter is a Professor in the Department of Statistics, University of Chicago.
Table of Contents
| Preface to the Second Edition | p. v |
| Preface to the First Edition | p. vii |
| Introduction | p. 1 |
| The Subject of Variance Estimation | p. 1 |
| The Scope and Organization of this Book | p. 4 |
| Notation and Basic Definitions | p. 6 |
| Standard Sampling Designs and Estimators | p. 11 |
| Linear Estimators | p. 16 |
| Survey Weights | p. 18 |
| The Method of Random Groups | p. 21 |
| Introduction | p. 21 |
| The Case of Independent Random Groups | p. 22 |
| Example: A Survey of AAA Motels | p. 28 |
| The Case of Nonindependent Random Groups | p. 32 |
| The Collapsed Stratum Estimator | p. 50 |
| Stability of the Random Group Estimator of Variance | p. 57 |
| Estimation Based on Order Statistics | p. 64 |
| Deviations from Strict Principles | p. 73 |
| On the Condition [theta] = [theta] for Linear Estimators | p. 84 |
| Example: The Retail Trade Survey | p. 86 |
| Example: The 1972-73 Consumer Expenditure Survey | p. 92 |
| Example: The 1972 Commodity Transportation Survey | p. 101 |
| Variance Estimation Based on Balanced Half-Samples | p. 107 |
| Introduction | p. 107 |
| Description of Basic Techniques | p. 108 |
| Usage with Multistage Designs | p. 113 |
| Usage with Nonlinear Estimators | p. 116 |
| Without Replacement Sampling | p. 119 |
| Partial Balancing | p. 123 |
| Extensions of Half-Sample Replication to the Case n[subscript h] [NotEqual] 2 | p. 128 |
| Miscellaneous Developments | p. 138 |
| Example: Southern Railway System | p. 139 |
| Example: The Health Examination Survey, Cycle II | p. 143 |
| The Jackknife Method | p. 151 |
| Introduction | p. 151 |
| Some Basic Infinite-Population Methodology | p. 152 |
| Basic Applications to the Finite Population | p. 162 |
| Application to Nonlinear Estimators | p. 169 |
| Usage in Stratified Sampling | p. 172 |
| Application to Cluster Sampling | p. 182 |
| Example: Variance Estimation for the NLSY97 | p. 185 |
| Example: Estimating the Size of the U.S. Population | p. 186 |
| The Bootstrap Method | p. 194 |
| Introduction | p. 194 |
| Basic Applications to the Finite Population | p. 196 |
| Usage in Stratified Sampling | p. 207 |
| Usage in Multistage Sampling | p. 210 |
| Nonlinear Estimators | p. 214 |
| Usage for Double Sampling Designs | p. 217 |
| Example: Variance Estimation for the NLSY97 | p. 221 |
| Taylor Series Methods | p. 226 |
| Introduction | p. 226 |
| Linear Approximations in the Infinite Population | p. 227 |
| Linear Approximations in the Finite Population | p. 230 |
| A Special Case | p. 233 |
| A Computational Algorithm | p. 234 |
| Usage with Other Methods | p. 235 |
| Example: Composite Estimators | p. 235 |
| Example: Simple Ratios | p. 240 |
| Example: Difference of Ratios | p. 244 |
| Example: Exponentials with Application to Geometric Means | p. 246 |
| Example: Regression Coefficients | p. 249 |
| Example: Poststratification | p. 257 |
| Example: Generalized Regression Estimator | p. 261 |
| Example: Logistic Regression | p. 265 |
| Example: Multilevel Analysis | p. 268 |
| Generalized Variance Functions | p. 272 |
| Introduction | p. 272 |
| Choice of Model | p. 273 |
| Grouping Items Prior to Model Estimation | p. 276 |
| Methods for Fitting the Model | p. 277 |
| Example: The Current Population Survey | p. 279 |
| Example: The Schools and Staffing Survey | p. 288 |
| Example: Baccalaureate and Beyond Longitudinal Study (B&B) | p. 290 |
| Variance Estimation for Systematic Sampling | p. 298 |
| Introduction | p. 298 |
| Alternative Estimators in the Equal Probability Case | p. 299 |
| Theoretical Properties of the Eight Estimators | p. 308 |
| An Empirical Comparison | p. 320 |
| Conclusions in the Equal Probability Case | p. 331 |
| Unequal Probability Systematic Sampling | p. 332 |
| Alternative Estimators in the Unequal Probability Case | p. 335 |
| An Empirical Comparison | p. 339 |
| Conclusions in the Unequal Probability Case | p. 351 |
| Summary of Methods for Complex Surveys | p. 354 |
| Accuracy | p. 355 |
| Flexibility | p. 364 |
| Administrative Considerations | p. 365 |
| Summary | p. 366 |
| Hadamard Matrices | p. 367 |
| Asymptotic Theory of Variance Estimators | p. 369 |
| Introduction | p. 369 |
| Case I: Increasing L | p. 370 |
| Case II: Increasing n[subscript h] | p. 374 |
| Bootstrap Method | p. 380 |
| Transformations | p. 384 |
| Introduction | p. 384 |
| How to Apply Transformations to Variance Estimation Problems | p. 385 |
| Some Common Transformations | p. 386 |
| An Empirical Study of Fisher's z-Transformation for the Correlation Coefficient | p. 389 |
| The Effect of Measurement Errors on Variance Estimation | p. 398 |
| Computer Software for Variance Estimation | p. 410 |
| The Effect of Imputation on Variance Estimation | p. 416 |
| Introduction | p. 416 |
| Inflation of the Variance | p. 417 |
| General-Purpose Estimators of the Variance | p. 421 |
| Multiple Imputation | p. 425 |
| Multiply Adjusted Imputation | p. 427 |
| Fractional Imputation | p. 429 |
| References | p. 433 |
| Index | p. 443 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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