Small area estimation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2003
|
| Series: | Wiley series in survey methodology
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XXIII, 313 S. |
| ISBN: | 0471413747 |
Staff View
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Record in the Search Index
| _version_ | 1804129483186241536 |
|---|---|
| adam_text | Titel: Small area estimation
Autor: Rao, Jonnagadda N. K
Jahr: 2003
Contents
List of Figures xiii
List of Tables xv
Foreword xvii
Preface xxi
1 Introduction 1
1.1 What is a Small Area?....................... 1
1.2 Demand for Small Area Statistics................. 3
1.3 Traditional Indirect Estimators.................. 3
1.4 Small Area Models......................... 4
1.5 Model-Based Estimation...................... 4
1.6 Some Examples........................... 6
2 Direct Domain Estimation 9
2.1 Introduction............................. 9
2.2 Design-based Approach ...................... 10
2.3 Estimation of Totals........................ 11
2.3.1 Design-unbiased Estimator ................ 11
2.3.2 Generalized Regression Estimator ............ 13
2.4 Domain Estimation......................... 15
2.4.1 Case of no Auxiliary Information............. 15
2.4.2 GREG Estimation..................... 17
2.4.3 Domain-specific Auxiliary Information.......... 17
2.5 Modified Direct Estimators.................... 20
2.6 Design Issues............................ 21
2.7 Proofs................................ 25
2.7.1 Proof of YGr(x) = X.................... 25
2.7.2 Derivation of Calibration Weights w* .......... 25
2.7.3 Proof of Y = XTB when Cj = i/tXj ........... 25
vu
viii CONTENTS
3 Traditional Demographic Methods 27
3.1 Introduction............................. 27
3.2 Symptomatic Accounting Techniques............... 28
3.2.1 Vital Rates Method.................... 28
3.2.2 Composite Method..................... 30
3.2.3 Component Methods.................... 30
3.2.4 Housing Unit Method................... 30
3.3 Regression Symptomatic Procedures............... 31
3.3.1 Ratio Correlation and Difference Correlation Methods . 31
3.3.2 Sample Regression Method................ 33
3.4 Dual-system Estimation of Total Population........... 37
3.4.1 Dual-system Model..................... 37
3.4.2 Post-enumeration Surveys................. 39
3.5 Derivation of Average MSEs.................... 42
4 Indirect Domain Estimation 45
4.1 Introduction............................. 45
4.2 Synthetic Estimation........................ 46
4.2.1 No Auxiliary Information................. 46
4.2.2 Auxiliary Information Available.............. 46
4.2.3 Regression-adjusted Synthetic Estimator......... 51
4.2.4 Estimation of MSE..................... 51
4.2.5 Structure Preserving Estimation............. 53
4.3 Composite Estimation....................... 57
4.3.1 Optimal Estimator..................... 57
4.3.2 Sample Size Dependent Estimators............ 60
4.4 James-Stein Method........................ 63
4.4.1 Common Weight...................... 63
4.4.2 Equal Variances fa ? i/ .................. 64
4.4.3 Estimation of Component MSE.............. 68
4.4.4 Unequal Variances fa ................... 71
4.4.5 Extensions ......................... 71
4.5 Proofs................................ 72
5 Small Area Models 75
5.1 Introduction............................. 75
5.2 Basic Area Level (Type A) Model ................ 76
5.3 Basic Unit Level (Type B) Model................. 78
5.4 Extensions: Type A Models.................... 81
5.4.1 Multivariate Fay-Herriot Model.............. 81
5.4.2 Model with Correlated Sampling Errors......... 82
5.4.3 Time Series and Cross-sectional Models......... 83
5.4.4 Spatial Models....................... 86
5.5 Extensions: Type B Models.................... 87
5.5.1 Multivariate Nested Error Regression Model....... 87
5.5.2 Random Error Variance Linear Model.......... 88
CONTENTS ix
5.5.3 Two-fold Nested Error Regression Model ........ 88
5.5.4 Two-level Model...................... 89
5.5.5 General Linear Mixed Model............... 90
5.6 Generalized Linear Mixed Models................. 91
5.6.1 Logistic Regression Models................ 91
5.6.2 Models for Mortality and Disease Rates......... 92
5.6.3 Exponential Family Models................ 93
5.6.4 Semi-parametric Models.................. 93
6 Empirical Best Linear Unbiased Prediction: Theory 95
6.1 Introduction............................. 95
6.2 General Linear Mixed Model ................... 96
6.2.1 BLUP Estimator...................... 96
6.2.2 MSE of BLUP....................... 98
6.2.3 EBLUP Estimator..................... 99
6.2.4 ML and REML Estimators................ 100
6.2.5 MSE of EBLUP ...................... 103
6.2.6 Estimation of MSE of EBLUP .............. 104
6.2.7 Software........................... 105
6.3 Block Diagonal Covariance Structure............... 107
6.3.1 EBLUP Estimator..................... 107
6.3.2 Estimation of MSE..................... 108
6.3.3 Extension.......................... 110
6.3.4 Model Diagnostics..................... 110
6.4 Proofs................................ 112
6.4.1 Derivation of BLUP.................... 112
6.4.2 Equivalence of BLUP and Best Predictor E(mrv|ATy) 113
6.4.3 Derivation of the Decomposition (6.2.26) ........ 113
7 EBLUP: Basic Models 115
7.1 Basic Area Level Model......................115
7.1.1 BLUP Estimator......................116
7.1.2 Estimation of a*......................118
7.1.3 Relative Efficiency of Estimators of a l..........120
7.1.4 Examples..........................121
7.1.5 MSE Estimation......................128
7.1.6 Conditional MSE......................131
7.1.7 Mean Product Error of Two Estimators.........132
7.1.8 Estimation of Small Area Means.............133
7.1.9 Weighted Estimator....................134
7.2 Basic Unit Level Model ......................134
7.2.1 BLUP Estimator......................135
7.2.2 Estimation of a% and a ..................138
7.2.3 MSE of EBLUP ......................139
7.2.4 MSE Estimation......................140
7.2.5 Non-negligible Sampling Rates..............141
CONTENTS
7.2.6 Examples..........................142
7.2.7 Pseudo-EBLUP Estimation................148
EBLUP: Extensions 153
8.1 Multivariate Fay-Herriot Model..................153
8.2 Correlated Sampling Errors....................155
8.3 Time Series and Cross-sectional Models.............158
8.3.1 Rao-Yu Model.......................158
8.3.2 State Space Models ....................162
8.4 Spatial Models...........................168
8.5 Multivariate Nested Error Regression Model...........169
8.6 Random Error Variances Linear Model..............171
8.7 Two-fold Nested Error Regression Model.............172
8.8 Two-level Model ..........................176
Empirical Bayes (EB) Method 179
9.1 Introduction.............................179
9.2 Basic Area Level Model......................180
9.2.1 EB Estimator........................181
9.2.2 MSE Estimation......................182
9.2.3 Approximation to Posterior Variance...........185
9.2.4 EB Confidence Intervals..................191
9.3 Linear Mixed Models........................194
9.3.1 EB Estimation.......................194
9.3.2 MSE Estimation......................195
9.3.3 Approximations to the Posterior Variance........196
9.4 Binary Data.............................197
9.4.1 Case of no Covariates...................197
9.4.2 Models with Covariates..................202
9.5 Disease Mapping..........................205
9.5.1 Poisson-Gamma Model ..................206
9.5.2 Log-normal Models.....................208
9.5.3 Extensions .........................209
9.6 Triple-goal Estimation.......................211
9.6.1 Constrained EB ......................211
9.6.2 Histogram..........................213
9.6.3 Ranks............................213
9.7 Empirical Linear Bayes ......................214
9.7.1 LB Estimation.......................214
9.7.2 Posterior Linearity.....................217
9.8 Constrained LB...........................219
9.9 Proofs................................220
9.9.1 Proof of (9.2.11)......................220
9.9.2 Proof of (9.2.30)......................221
9.9.3 Proof of (9.6.6).......................221
9.9.4 Proof of (9.7.1).......................222
CONTENTS xi
10 Hierarchical Bayes (HB) Method 223
10.1 Introduction............................. 223
10.2 MCMC Methods.......................... 224
10.2.1 Markov Chain ....................... 224
10.2.2 Gibbs Sampler....................... 225
10.2.3 M-H Within Gibbs..................... 226
10.2.4 Practical Issues....................... 227
10.2.5 Posterior Quantities.................... 230
10.2.6 Model Determination ................... 232
10.3 Basic Area Level Model...................... 237
10.3.1 Known a^.......................... 237
10.3.2 Unknown a%: Numerical Integration........... 237
10.3.3 Unknown a*: Gibbs Sampling............... 240
10.4 Unmatched Sampling and Linking Area Level Models ..... 243
10.5 Basic Unit Level Model ...................... 247
10.5.1 Known a2v and a ..................... 247
10.5.2 Unknown a% and a . Numerical Integration....... 247
10.5.3 Unknown a2 and a2: Gibbs Sampling .......... 248
10.5.4 Pseudo-HB Estimation................... 251
10.6 General ANOVA Model...................... 254
10.7 Two-level Models.......................... 255
10.8 Time Series and Cross-sectional Models............. 258
10.9 Multivariate Models........................ 263
10.9.1 Area Level Model...................... 263
10.9.2 Unit Level Model...................... 264
lO.lODisease Mapping Models...................... 264
10.10.1 Poisson-gamma Model................... 264
10.10.2 Log-normal Model..................... 265
10.10.3Two-level Models...................... 267
lO.HBinary Data............................. 269
10.11.1 Beta-binomial Model.................... 269
10.11.2Logit-normal Model.................... 270
10.11.3Logistic Linear Mixed Models............... 273
10.12Exponential Family Models.................... 277
10.13Constrained HB........................... 278
10.14Proofs................................ 279
10.14.1 Proof of (10.2.26)...................... 279
10.14.2Proof of (10.2.32)...................... 280
10.14.3Proof of (10.3.11)-(10.3.13)................ 280
References 283
Author Index 303
Subject Index 309
|
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| discipline | Mathematik Wirtschaftswissenschaften |
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| indexdate | 2024-07-09T19:05:51Z |
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| language | English |
| lccn | 2002033197 |
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| physical | XXIII, 313 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
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| publisher | Wiley |
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| series2 | Wiley series in survey methodology |
| spelling | Rao, J. N. K. 1937- Verfasser (DE-588)170433870 aut Small area estimation J. N. K. Rao Hoboken, NJ Wiley 2003 XXIII, 313 S. txt rdacontent n rdamedia nc rdacarrier Wiley series in survey methodology Includes bibliographical references and index Estimation, Théorie de l' Schattingen gtt Steekproeven gtt Échantillonnage (Statistique) Estimation theory Sampling (Statistics) Stichprobennahme (DE-588)4183250-4 gnd rswk-swf Schätztheorie (DE-588)4121608-8 gnd rswk-swf Stichprobennahme (DE-588)4183250-4 s Schätztheorie (DE-588)4121608-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009994080&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rao, J. N. K. 1937- Small area estimation Estimation, Théorie de l' Schattingen gtt Steekproeven gtt Échantillonnage (Statistique) Estimation theory Sampling (Statistics) Stichprobennahme (DE-588)4183250-4 gnd Schätztheorie (DE-588)4121608-8 gnd |
| subject_GND | (DE-588)4183250-4 (DE-588)4121608-8 |
| title | Small area estimation |
| title_auth | Small area estimation |
| title_exact_search | Small area estimation |
| title_full | Small area estimation J. N. K. Rao |
| title_fullStr | Small area estimation J. N. K. Rao |
| title_full_unstemmed | Small area estimation J. N. K. Rao |
| title_short | Small area estimation |
| title_sort | small area estimation |
| topic | Estimation, Théorie de l' Schattingen gtt Steekproeven gtt Échantillonnage (Statistique) Estimation theory Sampling (Statistics) Stichprobennahme (DE-588)4183250-4 gnd Schätztheorie (DE-588)4121608-8 gnd |
| topic_facet | Estimation, Théorie de l' Schattingen Steekproeven Échantillonnage (Statistique) Estimation theory Sampling (Statistics) Stichprobennahme Schätztheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009994080&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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