| Edition |
2nd ed |
| Descript |
1 online resource (476 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
Wiley Series in Survey Methodology Ser |
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Wiley Series in Survey Methodology Ser
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| Note |
Cover -- Title Page -- Copyright -- Dedication -- Contents -- List of Figures -- List of Tables -- Foreword to the First Edition -- Preface to the Second Edition -- Preface to the First Edition -- Chapter 1 *Introduction -- 1.1 What is a Small Area? -- 1.2 Demand for Small Area Statistics -- 1.3 Traditional Indirect Estimators -- 1.4 Small Area Models -- 1.5 Model-Based Estimation -- 1.6 Some Examples -- 1.6.1 Health -- 1.6.2 Agriculture -- 1.6.3 Income for Small Places -- 1.6.4 Poverty Counts -- 1.6.5 Median Income of Four-Person Families -- 1.6.6 Poverty Mapping -- Chapter 2 Direct Domain Estimation -- 2.1 Introduction -- 2.2 Design-Based Approach -- 2.3 Estimation of Totals -- 2.3.1 Design-Unbiased Estimator -- 2.3.2 Generalized Regression Estimator -- 2.4 Domain Estimation -- 2.4.1 Case of No Auxiliary Information -- 2.4.2 GREG Domain Estimation -- 2.4.3 Domain-Specific Auxiliary Information -- 2.5 Modified GREG Estimator -- 2.6 Design Issues -- 2.6.1 Minimization of Clustering -- 2.6.2 Stratification -- 2.6.3 Sample Allocation -- 2.6.4 Integration of Surveys -- 2.6.5 Dual-Frame Surveys -- 2.6.6 Repeated Surveys -- 2.7 *Optimal Sample Allocation for Planned Domains -- 2.7.1 Case (i) -- 2.7.2 Case (ii) -- 2.7.3 Two-Way Stratification: Balanced Sampling -- 2.8 Proofs -- 2.8.1 Proof of Ŷ GR(x) = X -- 2.8.2 Derivation of Calibration Weights wj* -- 2.8.3 Proof of Ŷ = X T B when cj = v T Xj -- Chapter 3 Indirect Domain Estimation -- 3.1 Introduction -- 3.2 Synthetic Estimation -- 3.2.1 No Auxiliary Information -- 3.2.2 *Area Level Auxiliary Information -- 3.2.3 *Unit Level Auxiliary Information -- 3.2.4 Regression-Adjusted Synthetic Estimator -- 3.2.5 Estimation of MSE -- 3.2.6 Structure Preserving Estimation -- 3.2.7 *Generalized SPREE -- 3.2.8 *Weight-Sharing Methods -- 3.3 Composite Estimation -- 3.3.1 Optimal Estimator |
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3.3.2 Sample-Size-Dependent Estimators -- 3.4 James-Stein Method -- 3.4.1 Common Weight -- 3.4.2 Equal Variances ψ i = ψ -- 3.4.3 Estimation of Component MSE -- 3.4.4 Unequal Variances ψ i -- 3.4.5 Extensions -- 3.5 Proofs -- Chapter 4 Small Area Models -- 4.1 Introduction -- 4.2 Basic Area Level Model -- 4.3 Basic Unit Level Model -- 4.4 Extensions: Area Level Models -- 4.4.1 Multivariate Fay-Herriot Model -- 4.4.2 Model with Correlated Sampling Errors -- 4.4.3 Time Series and Cross-Sectional Models -- 4.4.4 *Spatial Models -- 4.4.5 Two-Fold Subarea Level Models -- 4.5 Extensions: Unit Level Models -- 4.5.1 Multivariate Nested Error Regression Model -- 4.5.2 Two-Fold Nested Error Regression Model -- 4.5.3 Two-Level Model -- 4.5.4 General Linear Mixed Model -- 4.6 Generalized Linear Mixed Models -- 4.6.1 Logistic Mixed Models -- 4.6.2 *Models for Multinomial Counts -- 4.6.3 Models for Mortality and Disease Rates -- 4.6.4 Natural Exponential Family Models -- 4.6.5 *Semi-parametric Mixed Models -- Chapter 5 Empirical Best Linear Unbiased Prediction (EBLUP): Theory -- 5.1 Introduction -- 5.2 General Linear Mixed Model -- 5.2.1 BLUP Estimator -- 5.2.2 MSE of BLUP -- 5.2.3 EBLUP Estimator -- 5.2.4 ML and REML Estimators -- 5.2.5 MSE of EBLUP -- 5.2.6 Estimation of MSE of EBLUP -- 5.3 Block Diagonal Covariance Structure -- 5.3.1 EBLUP Estimator -- 5.3.2 Estimation of MSE -- 5.3.3 Extension to Multidimensional Area Parameters -- 5.4 *Model Identification and Checking -- 5.4.1 Variable Selection -- 5.4.2 Model Diagnostics -- 5.5 *Software -- 5.6 Proofs -- 5.6.1 Derivation of BLUP -- 5.6.2 Equivalence of BLUP and Best Predictor E(m Tv | A Ty) -- 5.6.3 Derivation of MSE Decomposition (5.2.29) -- Chapter 6 Empirical Best Linear Unbiased Prediction (EBLUP): Basic Area Level Model -- 6.1 EBLUP Estimation -- 6.1.1 BLUP Estimator -- 6.1.2 Estimation of σ v 2 |
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6.1.3 Relative Efficiency of Estimators of σ v 2 -- 6.1.4 *Applications -- 6.2 MSE Estimation -- 6.2.1 Unconditional MSE of EBLUP -- 6.2.2 MSE for Nonsampled Areas -- 6.2.3 *MSE Estimation for Small Area Means -- 6.2.4 *Bootstrap MSE Estimation -- 6.2.5 *MSE of a Weighted Estimator -- 6.2.6 Mean Cross Product Error of Two Estimators -- 6.2.7 *Conditional MSE -- 6.3 *Robust Estimation in the Presence of Outliers -- 6.4 *Practical Issues -- 6.4.1 Unknown Sampling Error Variances -- 6.4.2 Strictly Positive Estimators of σ v 2 -- 6.4.3 Preliminary Test Estimation -- 6.4.4 Covariates Subject to Sampling Errors -- 6.4.5 Big Data Covariates -- 6.4.6 Benchmarking Methods -- 6.4.7 Misspecified Linking Model -- 6.5 *Software -- Chapter 7 Basic Unit Level Model -- 7.1 EBLUP Estimation -- 7.1.1 BLUP Estimator -- 7.1.2 Estimation of σ v 2 and σ e 2 -- 7.1.3 *Nonnegligible Sampling Fractions -- 7.2 MSE Estimation -- 7.2.1 Unconditional MSE of EBLUP -- 7.2.2 Unconditional MSE Estimators -- 7.2.3 *MSE Estimation: Nonnegligible Sampling Fractions -- 7.2.4 *Bootstrap MSE Estimation -- 7.3 *Applications -- 7.4 *Outlier Robust EBLUP Estimation -- 7.4.1 Estimation of Area Means -- 7.4.2 MSE Estimation -- 7.4.3 Simulation Results -- 7.5 *M-Quantile Regression -- 7.6 *Practical Issues -- 7.6.1 Unknown Heteroscedastic Error Variances -- 7.6.2 Pseudo-EBLUP Estimation -- 7.6.3 Informative Sampling -- 7.6.4 Measurement Error in Area-Level Covariate -- 7.6.5 Model Misspecification -- 7.6.6 Semi-parametric Nested Error Model: EBLUP -- 7.6.7 Semi-parametric Nested Error Model: REBLUP -- 7.7 *Software -- 7.8 *Proofs -- 7.8.1 Derivation of (7.6.17) -- 7.8.2 Proof of (7.6.20) -- Chapter 8 EBLUP: Extensions -- 8.1 *Multivariate Fay-Herriot Model -- 8.2 Correlated Sampling Errors -- 8.3 Time Series and Cross-Sectional Models -- 8.3.1 *Rao-Yu Model -- 8.3.2 State-Space Models |
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8.4 *Spatial Models -- 8.5 *Two-Fold Subarea Level Models -- 8.6 *Multivariate Nested Error Regression Model -- 8.7 Two-Fold Nested Error Regression Model -- 8.8 *Two-Level Model -- 8.9 *Models for Multinomial Counts -- 8.10 *EBLUP for Vectors of Area Proportions -- 8.11 *Software -- Chapter 9 Empirical Bayes (EB) Method -- 9.1 Introduction -- 9.2 Basic Area Level Model -- 9.2.1 EB Estimator -- 9.2.2 MSE Estimation -- 9.2.3 Approximation to Posterior Variance -- 9.2.4 *EB Confidence Intervals -- 9.3 Linear Mixed Models -- 9.3.1 EB Estimation of μ i=l i Tβ+m i T v i -- 9.3.2 MSE Estimation -- 9.3.3 Approximations to the Posterior Variance -- 9.4 *EB Estimation of General Finite Population Parameters -- 9.4.1 BP Estimator Under a Finite Population -- 9.4.2 EB Estimation Under the Basic Unit Level Model -- 9.4.3 FGT Poverty Measures -- 9.4.4 Parametric Bootstrap for MSE Estimation -- 9.4.5 ELL Estimation -- 9.4.6 Simulation Experiments -- 9.5 Binary Data -- 9.5.1 *Case of No Covariates -- 9.5.2 Models with Covariates -- 9.6 Disease Mapping -- 9.6.1 Poisson-Gamma Model -- 9.6.2 Log-Normal Models -- 9.6.3 Extensions -- 9.7 *Design-Weighted EB Estimation: Exponential Family Models -- 9.8 Triple-Goal Estimation -- 9.8.1 Constrained EB -- 9.8.2 Histogram -- 9.8.3 Ranks -- 9.9 Empirical Linear Bayes -- 9.9.1 LB Estimation -- 9.9.2 Posterior Linearity -- 9.10 Constrained LB -- 9.11 *Software -- 9.12 Proofs -- 9.12.1 Proof of (9.2.11) -- 9.12.2 Proof of (9.2.30) -- 9.12.3 Proof of (9.8.6) -- 9.12.4 Proof of (9.9.1) -- Chapter 10 Hierarchical Bayes (HB) Method -- 10.1 Introduction -- 10.2 MCMC Methods -- 10.2.1 Markov Chain -- 10.2.2 Gibbs Sampler -- 10.2.3 M-H Within Gibbs -- 10.2.4 Posterior Quantities -- 10.2.5 Practical Issues -- 10.2.6 Model Determination -- 10.3 Basic Area Level Model -- 10.3.1 Known σ v 2 -- 10.3.2 *Unknown σ v 2 : Numerical Integration |
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10.3.3 Unknown σ v 2 : Gibbs Sampling -- 10.3.4 *Unknown Sampling Variances ψ i -- 10.3.5 *Spatial Model -- 10.4 *Unmatched Sampling and Linking Area Level Models -- 10.5 Basic Unit Level Model -- 10.5.1 Known σ v 2 and σ e 2 -- 10.5.2 Unknown σv 2 and σ e 2 : Numerical Integration -- 10.5.3 Unknown σ v 2 and σ e 2 : Gibbs Sampling -- 10.5.4 Pseudo-HB Estimation -- 10.6 General ANOVA Model -- 10.7 *HB Estimation of General Finite Population Parameters -- 10.7.1 HB Estimator under a Finite Population -- 10.7.2 Reparameterized Basic Unit Level Model -- 10.7.3 HB Estimator of a General Area Parameter -- 10.8 Two-Level Models -- 10.9 Time Series and Cross-Sectional Models -- 10.10 Multivariate Models -- 10.10.1 Area Level Model -- 10.10.2 Unit Level Model -- 10.11 Disease Mapping Models -- 10.11.1 Poisson-Gamma Model -- 10.11.2 Log-Normal Model -- 10.11.3 Two-Level Models -- 10.12 *Two-Part Nested Error Model -- 10.13 Binary Data -- 10.13.1 Beta-Binomial Model -- 10.13.2 Logit-Normal Model -- 10.13.3 Logistic Linear Mixed Models -- 10.14 *Missing Binary Data -- 10.15 Natural Exponential Family Models -- 10.16 Constrained HB -- 10.17 *Approximate HB Inference and Data Cloning -- 10.18 Proofs -- 10.18.1 Proof of (10.2.26) -- 10.18.2 Proof of (10.2.32) -- 10.18.3 Proof of (10.3.13)-(10.3.15) -- References -- Author Index -- Subject Index -- EULA |
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Description based on publisher supplied metadata and other sources |
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries |
| Link |
Print version: Rao, J. N. K. Small Area Estimation
: John Wiley & Sons, Incorporated,c2015 9781118735787
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| Subject |
Electronic books
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| Alt Author |
Molina, Isabel
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