Functional data analysis is a new area of statistical research, and these two leading figures present the first collection of methods in book-form. Much of the work is original to the authors. Bernard Silverman has been very successful in writing books at a level and a style that appeals to theoretical and applied audiences.

Klappentext

Included here are expressions in the functional domain of such classics as linear regression, principal components analysis, linear modelling, and canonical correlation analysis, as well as specifically functional techniques such as curve registration and principal differential analysis. Data arising in real applications are used throughout for both motivation and illustration, showing how functional approaches allow us to see new things, especially by exploiting the smoothness of the processes generating the data. The data sets exemplify the wide scope of functional data analysis; they are drawn from growth analysis, meteorology, biomechanics, equine science, economics, and medicine. The book presents novel statistical technology while keeping the mathematical level widely accessible. It is designed to appeal to students, applied data analysts, and to experienced researchers; and as such is of value both within statistics and across a broad spectrum of other fields. Much of the material appears here for the first time.

Inhalt

Introduction * Notation and Techniques * Representing Functional Data as Smooth Functions * The Roughness Penalty Approach * The Registration and Display of Functional Data * Principal Components Analysis for Functional Data * Regularized Principal Components Analysis * Principal Components Analysis of Mixed Data * Functional Linear Models * Functional Linear Models for Scalar Responses * Functional Linear Modesl for Functional Responses * Canonical Correlation and Discriminant Analysis * Differential Operators in Functional Data Analysis * Principal Differential Analysis * More General Roughness Penalties * Some Perspectives on FDA