Functional Data Analysis

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Springer Science & Business Media, Jun 28, 2006 - Mathematics - 428 pages
Scientists today 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 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 drwan from growth analysis, meterology, 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, to applied data analysts, and to experienced researchers; it will have value both within statistics and across a broad spectrum of other fields. Much of the material is based on the authors' own work, some of which appears here for the first time. Jim Ramsay is Professor of Psychology at McGill University and is an international authority on many aspects of multivariate analysis. He draws on his collaboration with researchers in speech articulation, motor control, meteorology, psychology, and human physiology to illustrate his technical contributions to functional data analysis in a wide range of statistical and application journals. Bernard Silverman, author of the highly regarded "Density Estimation for Statistics and Data Analysis," and coauthor of "Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach," is Professor of Statistics at Bristol University. His published work on smoothing methods and other aspects of applied, computational, and theoretical statistics has been recognized by the Presidents' Award of the Committee of Presidents of Statistical Societies, and the award of two Guy Medals by the Royal Statistical Society.
 

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Contents

incipal components analysis for functional data 147
2
v
11
Summary statistics for functional data
22
Phaseplane plots of periodic effects
29
om functional data to smooth functions
37
The Fourier basis system for periodic data
45
Other useful basis systems
53
noothing functional data by least squares
59
Computational issues
235
Further reading and notes
244
Longterm and seasonal trends in the nondurable goods
251
Confidence intervals
257
Regularization using restricted basis functions
264
The direct penalty method for computing 3
271
Further reading and notes
276
Assessing goodness of fit
290

noothing functional data with a roughness penalty
82
Confidence intervals for function values and functional
100
Further reading and notes
109
The performance of spline smoothing revisited
117
Fitting a linear model with estimation of the density
123
Shift registration
129
Using the warping function h to register ac
137
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144
Defining functional PCA
148
TfFQ
150
agularized principal components analysis
173
incipal components analysis of mixed data
187
The temperature data reconsidered
195
Principles of classical CCA
204
Algorithmic considerations
210
nctional linear models
217
Force plate data for walking horses
229
rivatives and functional linear models
297
JC0lD
305
Beyond the constant COff1C1Ilt first order linear equation
311
Some linear differential equation facts
319
Initial conditions boundary conditions and other con
323
A principal differential analysis of lip movement
329
Techniques for principal differential analysis
338
Further readings and notes
348
Further reading and notes
357
The optimal basis for spline smoothing
363
Some case studies
370
me perspectives on FDA 379
378
Some algebraic and functional techniques
385
Further aspects of inner product spaces
391
Kronecker Products
398
IlCS
405
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420

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