Wolter Introduction to Variance Estimation

1. Auflage 1985
ISBN: 978-0-387-35099-8
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 448 Seiten

Reihe: Springer Series in Statistics

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.

Autoren/Hrsg.

Wolter, Kirk

Inhaltsverzeichnis

1;Preface to the Second Edition;6
2;Preface to the First Edition;8
3;Contents;11
4;Introduction;15
4.1;1.1. The Subject of Variance Estimation;15
4.2;1.2. The Scope and Organization of this Book;18
4.3;1.3. Notation and Basic Definitions;20
4.4;1.4. Standard Sampling Designs and Estimators;25
4.5;1.5. Linear Estimators;30
4.6;1.6. Survey Weights;32
5;The Method of Random Groups;35
5.1;2.1. Introduction;35
5.2;2.2. The Case of Independent Random Groups;36
5.3;2.3. Example: A Survey of AAA Motels;42
5.4;2.4. The Case of Nonindependent Random Groups;46
5.5;2.5. The Collapsed Stratum Estimator;64
5.6;2.6. Stability of the Random Group Estimator of Variance;71
5.7;2.7. Estimation Based on Order Statistics;78
5.8;2.8. Deviations from Strict Principles;87
5.9;2.9. On the Condition ˆ¯ . = ˆ . for Linear Estimators;98
5.10;2.10. Example: The Retail Trade Survey;100
5.11;2.11. Example: The 1972-73 Consumer Expenditure Survey;106
5.12;2.12. Example: The 1972 Commodity Transportation Survey;115
6;Variance Estimation Based on Balanced Half- Samples;121
6.1;3.1. Introduction;121
6.2;3.2. Description of Basic Techniques;122
6.3;3.3. Usage with Multistage Designs;127
6.4;3.4. Usage with Nonlinear Estimators;130
6.5;3.5. Without Replacement Sampling;133
6.6;3.6. Partial Balancing;137
6.7;3.7. Extensions of Half-Sample Replication to the Case nh = 2;142
6.8;3.8. Miscellaneous Developments;152
6.9;3.9. Example: Southern Railway System;153
6.10;3.10. Example: The Health Examination Survey, Cycle II;157
7;The Jackknife Method;165
7.1;4.1. Introduction;165
7.2;4.2. Some Basic Infinite-Population Methodology;166
7.3;4.3. Basic Applications to the Finite Population;176
7.4;4.4. Application to Nonlinear Estimators;183
7.5;4.5. Usage in Stratified Sampling;186
7.6;4.6. Application to Cluster Sampling;196
7.7;4.7. Example: Variance Estimation for the NLSY97;199
7.8;4.8. Example: Estimating the Size of the U. S. Population;201
8;The Bootstrap Method;208
8.1;5.1. Introduction;208
8.2;5.2. Basic Applications to the Finite Population;210
8.3;5.3. Usage in Stratified Sampling;221
8.4;5.4. Usage in Multistage Sampling;224
8.5;5.5. Nonlinear Estimators;228
8.6;5.6. Usage for Double Sampling Designs;231
8.7;5.7. Example: Variance Estimation for the NLSY97;235
9;Taylor Series Methods;240
9.1;6.1. Introduction;240
9.2;6.2. Linear Approximations in the Infinite Population;241
9.3;6.3. Linear Approximations in the Finite Population;244
9.4;6.4. A Special Case;247
9.5;6.5. A Computational Algorithm;248
9.6;6.6. Usage with Other Methods;249
9.7;6.7. Example: Composite Estimators;249
9.8;6.8. Example: Simple Ratios;254
9.9;6.9. Example: Difference of Ratios;258
9.10;6.10. Example: Exponentials with Application to Geometric Means;260
9.11;6.11. Example: Regression Coefficients;263
9.12;6.12. Example: Poststratification;271
9.13;6.13. Example: Generalized Regression Estimator;275
9.14;6.14. Example: Logistic Regression;279
9.15;6.15. Example: Multilevel Analysis;282
10;Generalized Variance Functions;286
10.1;7.1. Introduction;286
10.2;7.2. Choice of Model;287
10.3;7.3. Grouping Items Prior to Model Estimation;290
10.4;7.4. Methods for Fitting the Model;291
10.5;7.5. Example: The Current Population Survey;293
10.6;7.6. Example: The Schools and Staffing Survey;302
10.7;7.7. Example: Baccalaureate and Beyond Longitudinal Study ( B& B);304
11;Variance Estimation for Systematic Sampling;312
11.1;8.1. Introduction;312
11.2;8.2. Alternative Estimators in the Equal Probability Case;313
11.3;8.3. Theoretical Properties of the Eight Estimators;322
11.4;8.4. An Empirical Comparison;334
11.5;8.5. Conclusions in the Equal Probability Case;345
11.6;8.6. Unequal Probability Systematic Sampling;346
11.7;8.7. Alternative Estimators in the Unequal Probability Case;349
11.8;8.8. An Empirical Comparison;353
11.9;8.9. Conclusions in the Unequal Probability Case;365
12;Summary of Methods for Complex Surveys;368
12.1;9.1. Accuracy;369
12.2;9.2. Flexibility;378
12.3;9.3. Administrative Considerations;379
12.4;9.4. Summary;380
13;Hadamard Matrices;381
14;Asymptotic Theory of Variance Estimators;383
14.1;B.1. Introduction;383
14.2;B.2. Case I: Increasing L;384
14.3;B.3. Case II: Increasing nh;388
14.4;B.4. Bootstrap Method;394
15;Transformations;398
15.1;C.1. Introduction;398
15.2;C.2. How to Apply Transformations to Variance Estimation Problems;399
15.3;C.3. Some Common Transformations;400
15.4;C.4. An Empirical Study of Fisher's z-Transformation for the Correlation Coefficient;403
16;The Effect of Measurement Errors on Variance Estimation;412
17;Computer Software for Variance Estimation;424
18;The Effect of Imputation on Variance Estimation;430
18.1;F.1. Introduction;430
18.2;F.2. Inflation of the Variance;431
18.3;F.3. General-Purpose Estimators of the Variance;435
18.4;F.4. Multiple Imputation;439
18.5;F.5. Multiply Adjusted Imputation;441
18.6;F.6. Fractional Imputation;443
19;References;446
20;Index;456