Introduction to Variance Estimation (eBook)
XIV, 448 Seiten
Springer New York (Verlag)
978-0-387-35099-8 (ISBN)
Now available in paperback, this book is organized in a way that emphasizes both the theory and applications of the various variance estimating techniques. Results are often presented in the form of theorems; proofs are deleted when trivial or when a reference is readily available. It applies to large, complex surveys; and to provide an easy reference for the survey researcher who is faced with the problem of estimating variances for real survey data.
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 andhas provided instruction in survey statistics both in America and around the world.
Preface to the Second Edition 6
Preface to the First Edition 8
Contents 11
Introduction 15
1.1. The Subject of Variance Estimation 15
1.2. The Scope and Organization of this Book 18
1.3. Notation and Basic Definitions 20
1.4. Standard Sampling Designs and Estimators 25
1.5. Linear Estimators 30
1.6. Survey Weights 32
The Method of Random Groups 35
2.1. Introduction 35
2.2. The Case of Independent Random Groups 36
2.3. Example: A Survey of AAA Motels 42
2.4. The Case of Nonindependent Random Groups 46
2.5. The Collapsed Stratum Estimator 64
2.6. Stability of the Random Group Estimator of Variance 71
2.7. Estimation Based on Order Statistics 78
2.8. Deviations from Strict Principles 87
2.9. On the Condition ˆ¯ . = ˆ . for Linear Estimators 98
2.10. Example: The Retail Trade Survey 100
2.11. Example: The 1972-73 Consumer Expenditure Survey 106
2.12. Example: The 1972 Commodity Transportation Survey 115
Variance Estimation Based on Balanced Half- Samples 121
3.1. Introduction 121
3.2. Description of Basic Techniques 122
3.3. Usage with Multistage Designs 127
3.4. Usage with Nonlinear Estimators 130
3.5. Without Replacement Sampling 133
3.6. Partial Balancing 137
3.7. Extensions of Half-Sample Replication to the Case nh = 2 142
3.8. Miscellaneous Developments 152
3.9. Example: Southern Railway System 153
3.10. Example: The Health Examination Survey, Cycle II 157
The Jackknife Method 165
4.1. Introduction 165
4.2. Some Basic Infinite-Population Methodology 166
4.3. Basic Applications to the Finite Population 176
4.4. Application to Nonlinear Estimators 183
4.5. Usage in Stratified Sampling 186
4.6. Application to Cluster Sampling 196
4.7. Example: Variance Estimation for the NLSY97 199
4.8. Example: Estimating the Size of the U. S. Population 201
The Bootstrap Method 208
5.1. Introduction 208
5.2. Basic Applications to the Finite Population 210
5.3. Usage in Stratified Sampling 221
5.4. Usage in Multistage Sampling 224
5.5. Nonlinear Estimators 228
5.6. Usage for Double Sampling Designs 231
5.7. Example: Variance Estimation for the NLSY97 235
Taylor Series Methods 240
6.1. Introduction 240
6.2. Linear Approximations in the Infinite Population 241
6.3. Linear Approximations in the Finite Population 244
6.4. A Special Case 247
6.5. A Computational Algorithm 248
6.6. Usage with Other Methods 249
6.7. Example: Composite Estimators 249
6.8. Example: Simple Ratios 254
6.9. Example: Difference of Ratios 258
6.10. Example: Exponentials with Application to Geometric Means 260
6.11. Example: Regression Coefficients 263
6.12. Example: Poststratification 271
6.13. Example: Generalized Regression Estimator 275
6.14. Example: Logistic Regression 279
6.15. Example: Multilevel Analysis 282
Generalized Variance Functions 286
7.1. Introduction 286
7.2. Choice of Model 287
7.3. Grouping Items Prior to Model Estimation 290
7.4. Methods for Fitting the Model 291
7.5. Example: The Current Population Survey 293
7.6. Example: The Schools and Staffing Survey 302
7.7. Example: Baccalaureate and Beyond Longitudinal Study ( B& B)
Variance Estimation for Systematic Sampling 312
8.1. Introduction 312
8.2. Alternative Estimators in the Equal Probability Case 313
8.3. Theoretical Properties of the Eight Estimators 322
8.4. An Empirical Comparison 334
8.5. Conclusions in the Equal Probability Case 345
8.6. Unequal Probability Systematic Sampling 346
8.7. Alternative Estimators in the Unequal Probability Case 349
8.8. An Empirical Comparison 353
8.9. Conclusions in the Unequal Probability Case 365
Summary of Methods for Complex Surveys 368
9.1. Accuracy 369
9.2. Flexibility 378
9.3. Administrative Considerations 379
9.4. Summary 380
Hadamard Matrices 381
Asymptotic Theory of Variance Estimators 383
B.1. Introduction 383
B.2. Case I: Increasing L 384
B.3. Case II: Increasing nh 388
B.4. Bootstrap Method 394
Transformations 398
C.1. Introduction 398
C.2. How to Apply Transformations to Variance Estimation Problems 399
C.3. Some Common Transformations 400
C.4. An Empirical Study of Fisher's z-Transformation for the Correlation Coefficient 403
The Effect of Measurement Errors on Variance Estimation 412
Computer Software for Variance Estimation 424
The Effect of Imputation on Variance Estimation 430
F.1. Introduction 430
F.2. Inflation of the Variance 431
F.3. General-Purpose Estimators of the Variance 435
F.4. Multiple Imputation 439
F.5. Multiply Adjusted Imputation 441
F.6. Fractional Imputation 443
References 446
Index 456
| Erscheint lt. Verlag | 13.8.2007 |
|---|---|
| Reihe/Serie | Springer Series in Statistics | Springer Series in Statistics |
| Zusatzinfo | XIV, 448 p. |
| Verlagsort | New York |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Statistik |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Technik | |
| Schlagworte | Estimator • Evaluation • Excel • Logistic Regression • Mathematical Statistics • Statistik |
| ISBN-10 | 0-387-35099-3 / 0387350993 |
| ISBN-13 | 978-0-387-35099-8 / 9780387350998 |
| Haben Sie eine Frage zum Produkt? |
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