Applied Functional Data Analysis

by Ramsay, J. O.; Silverman, B. W.

• ISBN13: 9780387954141
• ISBN10: 0387954147
• Format: Paperback
• Copyright: 2002-07-01
• Publisher: Springer Verlag

Summary

What do juggling, old bones, criminal careers and human growth patterns have in common? They all give rise to functional data, that come in the form of curves or functions rather than the numbers, or vectors of numbers, that are considered in conventional statistics. The authors' highly acclaimed book Functional Data Analysis (1997) presented a thematic approach to the statistical analysis of such data. By contrast, the present book introduces and explores the ideas of functional data analysis by the consideration of a number of case studies, many of them presented for the first time. The two books are complementary but neither is a prerequisite for the other. The case studies are accessible to research workers in a wide range of disciplines. Every reader, whether experienced researcher or graduate student, should gain not only a specific understanding of the methods of functional data analysis, but more importantly a general insight into the underlying patterns of thought. Some of the studies demand the development of novel aspects of the methodology of functional data analysis, but technical details aimed at the specialist statistician are confined to sections which the more general reader can safely omit. There is an associated web site with MATLAB and S-PLUS implementations of the methods discussed, together with all the data sets that are not proprietary. Jim Ramsay is Professor of Psychology at McGill University, and is an international authority on many aspects of multivariate analysis. He was elected President of the Statistical Society of Canada for the term 2002-3 and is a holder of the Society's Gold Medal for his work in functional data analysis. His statistical work draws on his collaborations with researchers in speech articulation, biomechanics, economics, human biology, meteorology and psychology. Bernard Silverman is Professor of Statistics at Bristol University. He was President of the Institute of Mathematical Statistics in 2000-1 and has held various offices in the Royal Statistical Society. He is a Fellow of the Royal Society and a member of Academia Europaea. His main specialty is computational statistics, and he is the author or editor of several highly regarded books in this area. He has also published widely in theoretical and applied statistics, and in many other fields, including law, human and veterinary medicine, earth sciences and engineering.

Author Biography

Bernard Silverman is Professor of Statistics at Bristol University.

Table of Contents

Preface	v
Introduction	1	(16)
Why consider functional data at all?	1	(1)
The Web site	2	(1)
The case studies	2	(12)
How is functional data analysis distinctive?	14	(1)
Conclusion and bibliography	15	(2)
Life Course Data in Criminology	17	(24)
Criminology life course studies	17	(2)
Background	17	(1)
The life course data	18	(1)
First steps in a functional approach	19	(4)
Turning discrete values into a functional datum	19	(2)
Estimating the mean	21	(2)
Functional principal component analyses	23	(8)
The basic methodology	23	(3)
Smoothing the PCA	26	(1)
Smoothed PCA of the criminology data	26	(2)
Detailed examination of the scores	28	(3)
What have we seen?	31	(2)
How are functions stored and processed?	33	(5)
Basis expansions	33	(2)
Fitting basis coefficients to the observed data	35	(1)
Smoothing the sample mean function	36	(1)
Calculations for smoothed functional PCA	37	(1)
Cross-validation for estimating the mean	38	(2)
Notes and bibliography	40	(1)
The Nondurable Goods Index	41	(16)
Introduction	41	(2)
Transformation and smoothing	43	(1)
Phase-plane plots	44	(3)
The nondurable goods cycles	47	(7)
What have we seen?	54	(1)
Smoothing data for phase-plane plots	55	(2)
Fourth derivative roughness penalties	55	(1)
Choosing the smoothing parameter	55	(2)
Bone Shapes from a Paleopathology Study	57	(12)
Archaeology and arthritis	57	(1)
Data capture	58	(1)
How are the shapes parameterized?	59	(2)
A functional principal components analysis	61	(2)
Procrustes rotation and PCA calculation	61	(1)
Visualizing the components of shape variability	61	(2)
Varimax rotation of the principal components	63	(2)
Bone shapes and arthritis: Clinical relationship?	65	(1)
What have we seen?	66	(1)
Notes and bibliography	66	(3)
Modeling Reaction-Time Distributions	69	(14)
Introduction	69	(2)
Nonparametric modeling of density functions	71	(2)
Estimating density and individual differences	73	(3)
Exploring variation across subjects with PCA	76	(3)
What have we seen?	79	(1)
Technical details	80	(3)
Zooming in on Human Growth	83	(18)
Introduction	83	(1)
Height measurements at three scales	84	(2)
Velocity and acceleration	86	(3)
An equation for growth	89	(2)
Timing or phase variation in growth	91	(2)
Amplitude and phase variation in growth	93	(3)
What we have seen?	96	(1)
Notes and further issues	97	(4)
Bibliography	97	(1)
The growth data	98	(1)
Estimating a smooth monotone curve to fit data	98	(3)
Time Warping Handwriting and Weather Records	101	(14)
Introduction	101	(1)
Formulating the registration problem	102	(2)
Registering the printing data	104	(1)
Registering the weather data	105	(5)
What have we seen?	110	(1)
Notes and references	110	(5)
Continuous registration	110	(3)
Estimation of the warping function	113	(2)
How Do Bone Shapes Indicate Arthritis?	115	(16)
Introduction	115	(1)
Analyzing shapes without landmarks	116	(4)
Investigating shape variation	120	(3)
Looking at means alone	120	(1)
Principal components analysis	120	(3)
The shape of arthritic bones	123	(5)
Linear discriminant analysis	123	(2)
Regularizing the discriminant analysis	125	(2)
Why not just look at the group means?	127	(1)
What have we seen?	128	(1)
Notes and further issues	128	(3)
Bibliography	128	(1)
Why is regularization necessary?	129	(1)
Cross-validation in classification problems	130	(1)
Functional Models for Test Items	131	(14)
Introduction	131	(1)
The ability space curve	132	(3)
Estimating item response functions	135	(1)
PCA of log odds-ratio functions	136	(2)
Do women and men perform differently on this test?	138	(2)
A nonlatent trait: Arc length	140	(3)
What have we seen?	143	(1)
Notes and bibliography	143	(2)
Predicting Lip Acceleration from Electromyography	145	(12)
The neural control of speech	145	(2)
The lip and EMG curves	147	(1)
The linear model for the data	148	(2)
The estimated regression function	150	(2)
How far back should the historical model go?	152	(3)
What have we seen?	155	(1)
Notes and bibliography	155	(2)
The Dynamics of Handwriting Printed Characters	157	(14)
Recording handwriting in real time	157	(1)
An introduction to dynamic models	158	(2)
One subject's printing data	160	(2)
A differential equation for handwriting	162	(3)
Assessing the fit of the equation	165	(1)
Classifying writers by using their dynamic equations	166	(4)
What have we seen?	170	(1)
A Differential Equation for Juggling	171	(12)
Introduction	171	(1)
The data and preliminary analyses	172	(1)
Features in the average cycle	173	(3)
The linear differential equation	176	(4)
What have we seen?	180	(1)
Notes and references	181	(2)
References	183	(4)
Index	187