*John C Gower and Garmt B Dijksterhuis*

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198510581
- eISBN:
- 9780191708961
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198510581.001.0001
- Subject:
- Mathematics, Probability / Statistics

Procrustean methods are used to transform one set of data to represent another set of data as closely as possible. This book unifies several strands in the literature and contains new algorithms. It ...
More

Procrustean methods are used to transform one set of data to represent another set of data as closely as possible. This book unifies several strands in the literature and contains new algorithms. It focuses on matching two or more configurations by using orthogonal, projection, and oblique axes transformations. Group-average summaries play an important part, and links with other group-average methods are discussed. The text is multi-disciplinary and also presents a unifying ANOVA framework.Less

Procrustean methods are used to transform one set of data to represent another set of data as closely as possible. This book unifies several strands in the literature and contains new algorithms. It focuses on matching two or more configurations by using orthogonal, projection, and oblique axes transformations. Group-average summaries play an important part, and links with other group-average methods are discussed. The text is multi-disciplinary and also presents a unifying ANOVA framework.

*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 ...
More

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.

*J. C. Gower and G. B. Dijksterhuis*

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198510581
- eISBN:
- 9780191708961
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198510581.003.0008
- Subject:
- Mathematics, Probability / Statistics

This chapter introduces the different forms of weighting. One form of weighting is when the rows of X1 are weighted. It is also possible to weight the columns. In these cases the ...
More

This chapter introduces the different forms of weighting. One form of weighting is when the rows of X1 are weighted. It is also possible to weight the columns. In these cases the weighting is expressed in terms of diagonal matrices. The most general form of weighting is when every cell of X1 gets separate weighting. Missing values may be specified by giving rows, columns, or cells zero weights. The important case of isotropic scaling is considered, where a scaling factor can be applied to the whole of the matrix X1 . This allows for the common situation where the relative sizes of X1 and X2 are unknown. Anisotropic scaling is introduced, represented by diagonal matrices S and T. Unlike weighting-matrices, which are given, scaling matrices need to be estimated. However, in iterative algorithms, the current estimates of scaling matrices may be treated as given weights while estimating updates of transformation matrices or further scaling matrices.Less

This chapter introduces the different forms of weighting. One form of weighting is when the *rows* of **X**_{1} are weighted. It is also possible to weight the columns. In these cases the weighting is expressed in terms of diagonal matrices. The most general form of weighting is when every cell of **X**_{1} gets separate weighting. Missing values may be specified by giving rows, columns, or cells zero weights. The important case of isotropic scaling is considered, where a scaling factor can be applied to the whole of the matrix **X**_{1} . This allows for the common situation where the relative sizes of **X**_{1} and **X**_{2} are unknown. Anisotropic *scaling* is introduced, represented by diagonal matrices **S** and **T**. Unlike weighting-matrices, which are given, scaling matrices need to be estimated. However, in iterative algorithms, the current estimates of scaling matrices may be treated as given weights while estimating updates of transformation matrices or further scaling matrices.

*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/9780198566625.003.0017
- Subject:
- Mathematics, Probability / Statistics

Using transformations in sample survey inference is the final chapter of this book and describes the extension of the empirical best prediction approach to the situation where the population values ...
More

Using transformations in sample survey inference is the final chapter of this book and describes the extension of the empirical best prediction approach to the situation where the population values of interest do not follow a linear model in their original scale of measurement, but can be transformed so that this is the case. In particular, it focuses on the situation where the logarithm of the survey variable can be modelled linearly, and develops methodology for correcting the transformation biases of empirical best predictors of the population mean. The logarithmic transformation is particularly useful when there are outliers in the data, and outlier robust versions of these predictors are developed. Empirical results based on actual business survey data are used to demonstrate the efficacy of the transformation-based predictors. Both estimation and sample design issues caused by model-misspecification in the transformed scale are also discussed.Less

Using transformations in sample survey inference is the final chapter of this book and describes the extension of the empirical best prediction approach to the situation where the population values of interest do not follow a linear model in their original scale of measurement, but can be transformed so that this is the case. In particular, it focuses on the situation where the logarithm of the survey variable can be modelled linearly, and develops methodology for correcting the transformation biases of empirical best predictors of the population mean. The logarithmic transformation is particularly useful when there are outliers in the data, and outlier robust versions of these predictors are developed. Empirical results based on actual business survey data are used to demonstrate the efficacy of the transformation-based predictors. Both estimation and sample design issues caused by model-misspecification in the transformed scale are also discussed.