This book contains the ideas of functional data analysis by a number of case studies. The case studies are accessible to research workers in a wide range of disciplines. Every reader 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. There is an associated web site with MATLABr and S?PLUSr implementations of the methods discussed.
Author(s): James O. Ramsay, Bernard W. Silverman
Series: Springer Series in Statistics
Edition: 1
Publisher: Springer
Year: 2002
Language: English
Pages: 201
APPLIED FUNCTIONAL DATA ANALYSIS: METHODS AND CASE STUDIES......Page 1
Springerlink......Page 0
Title Page......Page 3
Copyright Page......Page 5
Preface......Page 6
Contents......Page 8
1.1 Why consider functional data at all?......Page 12
1.3 The case studies......Page 13
1.4 How is functional data analysis distinctive?......Page 25
1.5 Conclusion and bibliography......Page 26
2.1.1 Background......Page 28
2.1.2 The life course data......Page 29
2.2.1 Turning discrete values into a functional datum......Page 30
2.2.2 Estimating the mean......Page 32
2.3.1 The basic methodology......Page 34
2.3.3 Smoothed PCA of the criminology data......Page 37
2.3.4 Detailed examination of the scores......Page 39
2.4 What have we seen?......Page 42
2.5.1 Basis expansions......Page 44
2.5.2 Fitting basis coefficients to the observed data......Page 46
2.5.3 Smoothing the sample mean function......Page 47
2.5.4 Calculations for smoothed functional PCA......Page 48
2.6 Cross-validation for estimating the mean......Page 49
2.7 Notes and bibliography......Page 51
3.1 Introduction......Page 52
3.2 Transformation and smoothing......Page 54
3.3 Phase-plane plots......Page 55
3.4 The nondurable goods cycles......Page 58
3.5 What have we seen?......Page 65
3.6.2 Choosing the smoothing parameter......Page 66
4.1 Archaeology and arthritis......Page 68
4.2 Data capture......Page 69
4.3 How are the shapes parameterized?......Page 70
4.4.2 Visualizing the components of shape variability......Page 72
4.5 Varimax rotation of the principal components......Page 74
4.6 Bone shapes and arthritis: Clinical relationship?......Page 76
4.8 Notes and bibliography......Page 77
5.1 Introduction......Page 80
5.2 Nonparametric modeling of density functions......Page 82
5.3 Estimating density and individual differences......Page 84
5.4 Exploring variation across subjects with PCA......Page 87
5.5 What have we seen?......Page 90
5.6 Technical details......Page 91
6.1 Introduction......Page 94
6.2 Height measurements at three scales......Page 95
6.3 Velocity and acceleration......Page 97
6.4 An equation for growth......Page 100
6.5 Timing or phase variation in growth......Page 102
6.6 Amplitude and phase variation in growth......Page 104
6.7 What we have seen?......Page 107
6.8.1 Bibliography......Page 108
6.8.3 Estimating a smooth monotone curve to fit data......Page 109
7.1 Introduction......Page 112
7.2 Formulating the registration problem......Page 113
7.3 Registering the printing data......Page 115
7.4 Registering the weather data......Page 116
7.6.1 Continuous registration......Page 121
7.6.2 Estimation of the warping function......Page 124
8.1 Introduction......Page 126
8.2 Analyzing shapes without landmarks......Page 127
8.3.2 Principal components analysis......Page 131
8.4.1 Linear discriminant analysis......Page 134
8.4.2 Regularizing the discriminant analysis......Page 136
8.4.3 Why not just look at the group means?......Page 138
8.6.1 Bibliography......Page 139
8.6.2 Why is regularization necessary?......Page 140
8.6.3 Cross-validation in classification problems......Page 141
9.1 Introduction......Page 142
9.2 The ability space curve......Page 143
9.3 Estimating item response functions......Page 146
9.4 PCA of log odds-ratio functions......Page 147
9.5 Do women and men perform differently on this test?......Page 149
9.6 A nonlatent trait: Arc length......Page 151
9.8 Notes and bibliography......Page 154
10.1 The neural control of speech......Page 156
10.2 The lip and EMG curves......Page 158
10.3 The linear model for the data......Page 159
10.4 The estimated regression function......Page 161
10.5 How far back should the historical model go?......Page 163
10.7 Notes and bibliography......Page 166
11.1 Recording handwriting in real time......Page 168
11.2 An introduction to dynamic models......Page 169
11.3 One subject’s printing data......Page 171
11.4 A differential equation for handwriting......Page 173
11.5 Assessing the fit of the equation......Page 176
11.6 Classifying writers by using their dynamic equations......Page 177
11.7 What have we seen?......Page 181
12.1 Introduction......Page 182
12.2 The data and preliminary analyses......Page 183
12.3 Features in the average cycle......Page 184
12.4 The linear differential equation......Page 187
12.5 What have we seen?......Page 191
12.6 Notes and references......Page 192
References......Page 194
Index......Page 198
