Ray Chambers and Robert Clark
- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780198566625
- eISBN:
- 9780191738449
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566625.001.0001
- Subject:
- Mathematics, Probability / Statistics
This book is an introduction to the model-based approach to survey sampling. It consists of three parts, with Part I focusing on estimation of population totals. Chapters 1 and 2 introduce survey ...
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This book is an introduction to the model-based approach to survey sampling. It consists of three parts, with Part I focusing on estimation of population totals. Chapters 1 and 2 introduce survey sampling, and the model-based approach, respectively. Chapter 3 considers the simplest possible model, the homogenous population model, which is then extended to stratified populations in Chapter 4. Chapter 5 discusses simple linear regression models for populations, and Chapter 6 considers clustered populations. The general linear population model is then used to integrate these results in Chapter 7. Part II of this book considers the properties of estimators based on incorrectly specified models. Chapter 8 develops robust sample designs that lead to unbiased predictors under model misspecification, and shows how flexible modelling methods like non-parametric regression can be used in survey sampling. Chapter 9 extends this development to misspecfication robust prediction variance estimators and Chapter 10 completes Part II of the book with an exploration of outlier robust sample survey estimation. Chapters 11 to 17 constitute Part III of the book and show how model-based methods can be used in a variety of problem areas of modern survey sampling. They cover (in order) prediction of non-linear population quantities, sub-sampling approaches to prediction variance estimation, design and estimation for multipurpose surveys, prediction for domains, small area estimation, efficient prediction of population distribution functions and the use of transformations in survey inference. The book is designed to be accessible to undergraduate and graduate level students with a good grounding in statistics and applied survey statisticians seeking an introduction to model-based survey design and estimation.Less
This book is an introduction to the model-based approach to survey sampling. It consists of three parts, with Part I focusing on estimation of population totals. Chapters 1 and 2 introduce survey sampling, and the model-based approach, respectively. Chapter 3 considers the simplest possible model, the homogenous population model, which is then extended to stratified populations in Chapter 4. Chapter 5 discusses simple linear regression models for populations, and Chapter 6 considers clustered populations. The general linear population model is then used to integrate these results in Chapter 7. Part II of this book considers the properties of estimators based on incorrectly specified models. Chapter 8 develops robust sample designs that lead to unbiased predictors under model misspecification, and shows how flexible modelling methods like non-parametric regression can be used in survey sampling. Chapter 9 extends this development to misspecfication robust prediction variance estimators and Chapter 10 completes Part II of the book with an exploration of outlier robust sample survey estimation. Chapters 11 to 17 constitute Part III of the book and show how model-based methods can be used in a variety of problem areas of modern survey sampling. They cover (in order) prediction of non-linear population quantities, sub-sampling approaches to prediction variance estimation, design and estimation for multipurpose surveys, prediction for domains, small area estimation, efficient prediction of population distribution functions and the use of transformations in survey inference. The book is designed to be accessible to undergraduate and graduate level students with a good grounding in statistics and applied survey statisticians seeking an introduction to model-based survey design and estimation.
Raymond L. Chambers and Robert G. Clark
- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780198566625
- eISBN:
- 9780191738449
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566625.003.0009
- Subject:
- Mathematics, Probability / Statistics
Robust estimation of the prediction variance discusses the issues that arise when model misspecification is second order. That is, when the second order moments of the working model for the ...
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Robust estimation of the prediction variance discusses the issues that arise when model misspecification is second order. That is, when the second order moments of the working model for the population are incorrect, as is typically the case. Here balanced sampling is of no avail, and alternative, more robust, methods of prediction variance must be used. This chapter focuses on development of these methods for the case where the working population model is the ratio model, as well as when a general linear predictor is used and the working model has quite general first and second order moments. The case of a clustered population with unknown within cluster heteroskedasticity is also discussed and the ultimate cluster variance estimator derived.Less
Robust estimation of the prediction variance discusses the issues that arise when model misspecification is second order. That is, when the second order moments of the working model for the population are incorrect, as is typically the case. Here balanced sampling is of no avail, and alternative, more robust, methods of prediction variance must be used. This chapter focuses on development of these methods for the case where the working population model is the ratio model, as well as when a general linear predictor is used and the working model has quite general first and second order moments. The case of a clustered population with unknown within cluster heteroskedasticity is also discussed and the ultimate cluster variance estimator derived.
Christopher G. Small and Jinfang Wang
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198506881
- eISBN:
- 9780191709258
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506881.003.0002
- Subject:
- Mathematics, Probability / Statistics
This chapter gives a survey of the basic concepts of estimating functions, which are used in subsequent chapters. The concept of unbiasedness for estimating functions is introduced as a ...
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This chapter gives a survey of the basic concepts of estimating functions, which are used in subsequent chapters. The concept of unbiasedness for estimating functions is introduced as a generalization of the concept of an unbiased estimator. Godambe efficiency, also known as the Godambe optimality criterion, is introduced by generalizing the concept of minimum variance unbiased estimation. Within the class of estimating functions which are unbiased and information unbiased, the score function is characterized as the estimating function with maximal Godambe efficiency. Extensions to the multiparameter case are given, and the connection to the Riesz representation theorem is described briefly. This chapter also discusses a number of examples from semiparametric models, martingale estimating functions for stochastic processes, empirical characteristic function methods and quadrat sampling; the estimating equations in some of these examples have possibly more than one solution.Less
This chapter gives a survey of the basic concepts of estimating functions, which are used in subsequent chapters. The concept of unbiasedness for estimating functions is introduced as a generalization of the concept of an unbiased estimator. Godambe efficiency, also known as the Godambe optimality criterion, is introduced by generalizing the concept of minimum variance unbiased estimation. Within the class of estimating functions which are unbiased and information unbiased, the score function is characterized as the estimating function with maximal Godambe efficiency. Extensions to the multiparameter case are given, and the connection to the Riesz representation theorem is described briefly. This chapter also discusses a number of examples from semiparametric models, martingale estimating functions for stochastic processes, empirical characteristic function methods and quadrat sampling; the estimating equations in some of these examples have possibly more than one solution.
Raymond L. Chambers and Robert G. Clark
- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780198566625
- eISBN:
- 9780191738449
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566625.003.0012
- Subject:
- Mathematics, Probability / Statistics
Survey inference via sub-sampling describes the different resampling approaches that can be used in finite population inference. It starts with a discussion of the interpenetrated sampling idea that ...
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Survey inference via sub-sampling describes the different resampling approaches that can be used in finite population inference. It starts with a discussion of the interpenetrated sampling idea that underlies the independent sub-groups methods of variance estimation, then moves on to the popular jackknife method, which uses the variation between dependent subgroups to estimate the prediction variance of a complex estimator. A linearised version of the jackknife that avoids its heavy computational burden in large samples is described. The bootstrap technique is finally introduced and two variants, the naive unconditional bootstrap and the conditional model-based bootstrap, are discussed. A modification to the latter bootstrap that makes it robust to misspecification of the second order properties of the working model for the population is proposed.Less
Survey inference via sub-sampling describes the different resampling approaches that can be used in finite population inference. It starts with a discussion of the interpenetrated sampling idea that underlies the independent sub-groups methods of variance estimation, then moves on to the popular jackknife method, which uses the variation between dependent subgroups to estimate the prediction variance of a complex estimator. A linearised version of the jackknife that avoids its heavy computational burden in large samples is described. The bootstrap technique is finally introduced and two variants, the naive unconditional bootstrap and the conditional model-based bootstrap, are discussed. A modification to the latter bootstrap that makes it robust to misspecification of the second order properties of the working model for the population is proposed.
