Functional Data Analysis / by James Ramsay, B. W. Silverman.

Format:

Book

Author/Creator:

Ramsay, J. O. (James O.)

Contributor:

Silverman, B. W., 1952-

Series:

Springer Series in Statistics, 2197-568X

Language:

English

Subjects (All):

Statistics.

Statistical Theory and Methods.

Local Subjects:

Statistical Theory and Methods.

Physical Description:

1 online resource (xix, 426 pages) : illustrations

Edition:

2nd ed. 2005.

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 2005.

Language Note:

English

Summary:

Scientists and others today often collect samples of curves and other functional observations. This monograph presents many ideas and techniques for such data. Included are expressions in the functional domain of such classics as linear regression, principal components analysis, linear modeling, 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, much of it based on the authors’ own research work, while keeping the mathematical level widely accessible. It is designed to appeal to students, to applied data analysts, and to experienced researchers; it will have value both within statistics and across a broad spectrum of other fields. This second edition is aimed at a wider range of readers, and especially those who would like to apply these techniques to their research problems. It complements the authors' other recent volume Applied Functional Data Analysis: Methods and Case Studies. In particular, there is an extended coverage of data smoothing and other matters arising in the preliminaries to a functional data analysis. The chapters on the functional linear model and modeling of the dynamics of systems through the use of differential equations and principal differential analysis have been completely rewritten and extended to include new developments. Other chapters have been revised substantially, often to give more weight to examples and practical considerations. Jim Ramsay is Professor of Psychology at McGill University and is an international authority on many aspects of multivariate analysis. He was President of the Statistical Society of Canada in 2002-3 and holds the Society’s Gold Medal for his work in functional data analysis. Bernard Silverman is Master of St Peter’s College and Professor of Statistics at Oxford University. He was President of the Institute of Mathematical Statistics in 2000–1. He is a Fellow of the Royal Society. His main specialty is in computational statistics, and he is the author or editor of several highly regarded books in this area. .

Contents:

Tools for exploring functional data

From functional data to smooth functions

Smoothing functional data by least squares

Smoothing functional data with a roughness penalty

Constrained functions

The registration and display of functional data

Principal components analysis for functional data

Regularized principal components analysis

Principal components analysis of mixed data

Canonical correlation and discriminant analysis

Functional linear models

Modelling functional responses with multivariate covariates

Functional responses, functional covariates and the concurrent model

Functional linear models for scalar responses

Functional linear models for functional responses

Derivatives and functional linear models

Differential equations and operators

Fitting differential equations to functional data: Principal differential analysis

Green’s functions and reproducing kernels

More general roughness penalties

Some perspectives on FDA.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. [293]-302) and index.

ISBN:

9786610612420

9786610006854

9780387400808

038740080X

9781601193094

1601193092

9781280006852

1280006854

9781280612428

1280612428

9780387227511

0387227512

OCLC:

209836083