Applied Functional Data Analysis: Methods and Case Studies

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Springer, Nov 23, 2007 - Mathematics - 191 pages
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Almost as soon as we had completed our previous book Functional Data Analysis in 1997, it became clear that potential interest in the ?eld was far wider than the audience for the thematic presentation we had given there. At the same time, both of us rapidly became involved in relevant new research involving many colleagues in ?elds outside statistics. This book treats the ?eld in a di?erent way, by considering case st- ies arising from our own collaborative research to illustrate how functional data analysis ideas work out in practice in a diverse range of subject areas. These include criminology, economics, archaeology, rheumatology, psych- ogy, neurophysiology, auxology (the study of human growth), meteorology, biomechanics, and education—and also a study of a juggling statistician. Obviously such an approach will not cover the ?eld exhaustively, and in any case functional data analysis is not a hard-edged closed system of thought. Nevertheless we have tried to give a ?avor of the range of meth- ology we ourselves have considered. We hope that our personal experience, including the fun we had working on these projects, will inspire others to extend “functional” thinking to many other statistical contexts. Of course, manyofourcasestudiesrequireddevelopmentofexistingmethodology,and readersshouldgaintheabilitytoadaptmethodstotheirownproblemstoo.
 

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Contents

Introduction
1
12 The Web site
2
14 How is functional data analysis distinctive?
14
15 Conclusion and bibliography
15
Life Course Data in Criminology
17
212 The life course data
18
22 First steps in a functional approach
19
222 Estimating the mean
21
682 The growth data
98
Time Warping Handwriting and Weather Records
101
72 Formulating the registration problem
102
73 Registering the printing data
104
74 Registering the weather data
105
75 What have we seen?
110
762 Estimation of the warping function
113
How Do Bone Shapes Indicate Arthritis?
115

23 Functional principal component analyses
23
232 Smoothing the PCA
26
234 Detailed examination of the scores
28
24 What have we seen?
31
25 How are functions stored and processed?
33
252 Fitting basis coefficients to the observed data
35
253 Smoothing the sample mean function
36
254 Calculations for smoothed functional PC A
37
26 Crossvalidation for estimating the mean
38
27 Notes and bibliography
40
The Nondurable Goods Index
41
32 Transformation and smoothing
43
33 Phaseplane plots
44
34 The nondurable goods cycles
47
35 What have we seen?
54
36 Smoothing data for phaseplane plots
55
Bone Shapes from a Paleopathology Study
57
42 Data capture
58
43 How are the shapes parameterized?
59
44 A functional principal components analysis
61
45 Varimax rotation of the principal components
63
Clinical relationship?
65
47 What have we seen?
66
Modeling ReactionTime Distributions
69
52 Nonparametric modeling of density functions
71
53 Estimating density and individual differences
73
54 Exploring variation across subjects with PCA
76
55 What have we seen?
79
56 Technical details
80
Zooming in on Human Growth
82
62 Height measurements at three scales
84
63 Velocity and acceleration
86
64 An equation for growth
89
65 Timing or phase variation in growth
91
66 Amplitude and phase variation in growth
93
67 What we have seen?
96
68 Notes and further issues
97
82 Analyzing shapes without landmarks
116
83 Investigating shape variation
120
84 The shape of arthritic bones
123
842 Regularizing the discriminant analysis
125
843 Why not just look at the group means?
127
85 What have we seen?
128
862 Why is regularization necessary?
129
863 Crossvalidation in classification problems
130
Functional Models for Test Items
131
92 The ability space curve
132
93 Estimating item response functions
135
94 PCA of log oddsratio functions
136
95 Do women and men perform differently on this test?
138
Arc length
140
97 What have we seen?
143
Predicting Lip Acceleration from Electromyography
144
102 The lip and EMG curves
147
103 The linear model for the data
148
104 The estimated regression function
150
105 How far back should the historical model go?
152
106 What have we seen?
155
The Dynamics of Handwriting Printed Characters
157
112 An introduction to dynamic models
158
113 One subjects printing data
160
114 A differential equation for handwriting
162
115 Assessing the fit of the equation
165
116 Classifying writers by using their dynamic equations
166
117 What have we seen?
170
A Differential Equation for Juggling
171
122 The data and preliminary analyses
172
123 Features in the average cycle
173
124 The linear differential equation
176
125 What have we seen?
180
126 Notes and references
181
References
183
Index
187
Copyright

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Page 185 - Growth, Maturation and Body Composition: The Fels Longitudinal Study 1929-1991. Cambridge: Cambridge University Press, 1992.
Page 185 - Ramsay, JO (2000). Functional components of variation in handwriting. Journal of the American Statistical Association, 95, 9-15. Ramsay, JO and Bock, RD (2002).
Page 185 - Ramsay, JO, Bock, RD, and Gasser, T. (1995). Comparison of height acceleration curves in the Fels, Zurich, and Berkeley growth data. Annals of Human Biology, 22, 413-426.
Page 186 - Foster, PJ, Gill, MS, Price, DA, and Clayton, P. E. (1996). Model of normal prepubertal growth.

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