Atkinson / Riani / Cerioli Exploring Multivariate Data with the Forward Search

2004
ISBN: 978-0-387-21840-3
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 624 Seiten, eBook

Reihe: Springer Series in Statistics

This book is concerned with data in which the observations are independent and in which the response is multivariate.

Companion book to Robust Diagnostic Regression Analysis (ISBN 0-387-95017) published by Springer in 2000.

Zielgruppe

Research

Autoren/Hrsg.

Atkinson, Anthony C.

Riani, Marco

Cerioli, Andrea

Inhaltsverzeichnis

Contents
Preface

Notation

1 Examples of Multivariate Data

1.1 In.uence, Outliers and Distances

1.2 A Sketch of the Forward Search

1.3 Multivariate Normality and our Examples

1.4 Swiss Heads

1.5 National Track Records forWomen

1.6 Municipalities in Emilia-Romagna

1.7 Swiss Bank Notes

1.8 Plan of the Book 2 Multivariate Data and the Forward Search

2.1 The Univariate Normal Distribution

2.1.1 Estimation

2.1.2 Distribution of Estimators

2.2 Estimation and the Multivariate Normal Distribution

2.2.1 The Multivariate Normal Distribution

2.2.2 The Wishart Distribution

2.2.3 Estimation of Ó
2.3 Hypothesis Testing

2.3.1 Hypotheses About the Mean

2.3.2 Hypotheses About the Variance

2.4 The Mahalanobis Distance

2.5 Some Deletion Results

2.5.1 The Deletion Mahalanobis Distance

2.5.2 The (Bartlett)-Sherman-Morrison-Woodbury Formula

2.5.3 Deletion Relationships Among Distances

2.6 Distribution of the Squared Mahalanobis Distance

2.7 Determinants of Dispersion Matrices and the Squared Mahalanobis Distance

2.8 Regression

2.9 Added Variables in Regression

2.10 TheMean Shift OutlierModel

2.11 Seemingly Unrelated Regression

2.12 The Forward Search

2.13 Starting the Search

2.13.1 The Babyfood Data

2.13.2 Robust Bivariate Boxplots from Peeling

2.13.3 Bivariate Boxplots from Ellipses

2.13.4 The Initial Subset

2.14 Monitoring the Search

2.15 The Forward Search for Regression Data

2.15.1 Univariate Regression

2.15.2 Multivariate Regression

2.16 Further Reading

2.17 Exercises

2.18 Solutions 3 Data from One Multivariate Distribution

3.1 Swiss Heads

3.2 National Track Records for Women

3.3 Municipalities in Emilia-Romagna

3.4 Swiss Bank Notes

3.5 What Have We Seen?

3.6 Exercises

3.7 Solutions 4 Multivariate Transformations to Normality

4.1 Background
4.2 An Introductory Example: the Babyfood Data

4.3 Power Transformations to Approximate Normality

4.3.1 Transformation of the Response in Regression

4.3.2 Multivariate Transformations to Normality

4.4 Score Tests for Transformations

4.5 Graphics for Transformations

4.6 Finding a Multivariate Transformation with the Forward Search

4.7 Babyfood Data

4.8 Swiss Heads

4.9 Horse Mussels

4.10 Municipalities in Emilia-Romagna

4.10.1 Demographic Variables

4.10.2 Wealth Variables

4.10.3 Work Variables

4.10.4 A Combined Analysis

4.11 National Track Records for Women

4.12 Dyestuff Data

4.13 Babyfood Data and Variable Selection

4.14 Suggestions for Further Reading

4.15 Exercises

4.16 Solutions 5 Principal Components Analysis

5.1 Background

5.2 Principal Components and Eigenvectors

5.2.1 Linear Transformations and Principal Components .

5.2.2 Lack of Scale Invariance and Standardized Variables

5.2.3 The Number of Components

5.3 Monitoring the Forward Search

5.3.1 Principal Components and Variances

5.3.2 Principal Component Scores

5.3.3 Correlations Between Variables and Principal Components

5.3.4 Elements of the Eigenvectors

5.4 The Biplot and the Singular Value Decomposition

5.5 Swiss Heads

5.6 Milk Data

5.7 Quality of Life

5.8 Swiss Bank Notes

5.8.1 Forgeries and Genuine Notes

5.8.2 Forgeries Alone

5.9 Municipalities in Emilia-Romagna

5.10 Further reading

5.11 Exercises

5.12 Solutions 6 Discriminant Analysis

6.1 Background

6.2 An Outline of Discriminant Analysis

6.2.1 Bayesian Discrimination

6.2.2 Quadratic Discriminant Analysis

6.2.3 Linear Discriminant Analysis

6.2.4 Estimation of Means and Variances

6.2.5 Canonical Variates

6.2.6 Assessment of Discriminant Rules

6.3 The Forward Search

6.3.1 Step 1: Choice of the Initial Subset

6.3.2 Step 2: Adding