Atkinson A.C., Riani M., Cerioli A. Exploring Multivariate Data with the Forward Search

Springer, 2004. — 623 p. — ISBN: 978-1-4419-2353-0, e-ISBN: 978-0-387-21840-3.Series: Springer Series in Statistics.The forward search provides a method of revealing the structure of data through a mixture of model fitting and informative plots. The continuous multivariate data that are the subject of this book are often analyzed as if they come from one or more normal distributions. Such analyses, including the need for transformation, may be distorted by the presence of unidentified subsets and outliers, both individual and clustered. These important features are disguised by the standard procedures of multivariate analysis. The book introduces methods that reveal the effect of each observation on fitted models and inferences.The powerful methods of data analysis will be of importance to scientists and statisticians. Although the emphasis is on the analysis of data, theoretical developments make the book suitable for a graduate statistical course on multivariate analysis. Topics covered include principal components analysis, discriminant analysis, cluster analysis and the analysis of spatial data.Examples of Multivariate Data.Infiuence, Outliers and Distauces; A Sketch of the Forward Search, Multivariate Normality and our Examples, Swiss Heads, National Track Records for Women, Municipalities in Emilia-Romagna, Swiss Bank Notes,Plan of the Book.
Multivariate Data and the Forward Search.
The Univariate Normal Distribution: Estimation, Distribution of Estimators;
Estimation and the Multivariate Normal Distribution:
The Multivariate Normal Distribution, The Wishart Distribution, Estimation of Σ;
Hypothesis Testing: Hypotheses About the Mean, Hypotheses About the Variance;
The Mahalanobis Distance, Some Deletion Results, Distribution of the Squared Mahalanobis Distance,
Determinants of Dispersion Matrices and the Squared, Mahalanobis Distance,
Regression, Added Variables in Regression, The Mean Shift Outlier Model, Seemingly Unrelated Regression,
The Forward Search, Starting the Search, Monitoring the Search, The Forward Search for Regression Data.
Data from One Multivariate Distribution.
Swiss Heads, National Track Records for Women, Municipalities in Emilia-Romagna, Swiss Bank Notes, What Have We Seen?
Multivariate Transformations to Normality.
An Introductory Example: the Babyfood Data, Power Transformations to Approximate Normality,
Score Tests for Transformations, Graphics for Transformations, Finding a Multivariate Thansformation with the Forward Search,
Babyfood Data, Swiss Heads, Horse Musseis, Municipalities in Emilia-Romagna,
NationalThack Records for Women, Dyestuff Data, Babyfood Data and Variable Selection, Suggestions for Further Reading.
Principal Components Analysis.
Principal Components and Eigenvectors, Monitaring the Forward Search,
The Biplot and the Singular Value Decomposition,
Swiss Heads, Milk Data, Quality of Life, Swiss Bank Notes, Municipalities in Emilia-Romagna.
Discriminant Analysis.
An Outline of Discriminant Analysis:
Bayesian Discrimination, Quadratic Discriminant Analysis, Linear Discriminant Analysis,
Estimation of Means and Variances, Canonical Variates, Assessment of Discriminant Rules;
The Forward Search, Monitoring the Search, Transformations to Normality in Discriminant Analysis,
Iris Data, Electrodes Data, Transformed Iris Data, Swiss Bank Notes,
Importance of Transformations in Discriminant Analysis, Muscular Dystrophy Data.
Cluster Analysis.
Clustering and the Forward Search, The 60:80 Data, Three Clusters, Two Outliers: A Second Synthetic Example,
Data with a Bridge, Financial Data, Diabetes Data, Discussion:
Agglomerative Hierarchical Clustering, Partitioning Methods,
Same Examples from Traditional Cluster Analysis, Model-Based Clustering.
Spatial Linear Models.
Background on Kriging:
Ordinary Kriging, Isotropie Semivariogram Models, Spatial Outliers, Kriging Diagnostics, Robust Estimation of the Variagram;
The Forward Search for Ordinary Kriging, Contaminated Kriging Examples, Wheat Yield Data,
Reflectance Data, Background on Spatial Autoregression, The Block Forward Search for Spatial Autoregression,
SAR Examples With Multiple Cantamination, Wheat Yield Data Revisited.
Appendix: Tables of Data.