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【资料名称】：Applied Functional Data Analysis--Methods and Case Studies
【资料作者】： J.O. Ramsay, B.W. Silverman
【出版社】： Springer
【简介及目录】：
Product Details
- Paperback: 200 pages
- Publisher: Springer; 1 edition (June 13, 2002)
- Language: English
- ISBN-10: 0387954147
Review
From the reviews:
"Analysis of functional data has become a very active area of research in statistics. … Examples discussed in the book are extremely well chosen.Theyreally make the book a very enjoyable reading. This book will surelyattract more people into the area of functional data analysis. …theauthors have done a commendable job of exposing functional dataanalysis through a wide variety of examples chosen from diverse fields…. I expect this book to be widely read and referenced in near future."(Probal Chaudhuri, Sankhya, Vol. 63 (4), 2003)
"This book is a follow-up to the monograph Functional Data Analysis(FDA) by the same authors. … This is an unusual book, an interestingbook in afield which is still in expansion and where lots of data setswill come up in the future. The data sets and the data analyses arevaried and thought-provoking. … the appropriate audience would begraduate students, statistical researchers, and experienced appliedstatisticians." (Theo Gasser, SIAM Review, Vol. 45 (2), 2003)
"The best-known opportunity for functional data analysis (FDA) iswhen the data are measurements of a continuous function of time, orsome other continuous variable. However, the authors show that therange of application can be much wider. … One of the attractions ofthis book is the range of examples … . Overall, the book achieves wellits main objective of showing what FDA can do. I hope that it succeedsin encouraging the use of powerful data analysis techniques in newapplication areas." (Tim Auton, Journal of the Royal StatisticalSociety, Vol. 157 (2), 2004)
"This book deals with functional data analysis from a very appliedpoint of view. … The mentioned case studies are accessible to workersin a wide range of disciplines. …Therefore, the non mathematicallyoriented audience will enjoy reading through it … ." (Henri Schurz,Zentralblatt MATH, Vol. 1011, 2003)
Product Description
What do juggling, old bones, criminal careers and human growth patternshave in common? They all give rise to functional data, that come in theform of curves or functions rather than the numbers, or vectors ofnumbers, that are considered in conventional statistics. The authors'highly acclaimed book Functional Data Analysis (1997) presenteda thematic approach to the statistical analysis of such data. Bycontrast, the present book introduces and explores the ideas offunctional data analysis by the consideration of a number of casestudies, many of them presented for the first time. The two books arecomplementary but neither is a prerequisite for the other. The casestudies are accessible to research workers in a wide range ofdisciplines. Every reader, whether experienced researcher or graduatestudent, should gain not only a specific understanding of the methodsof functional data analysis, but more importantly a general insightinto the underlying patterns of thought. Some of the studies demand thedevelopment of novel aspects of the methodology of functional dataanalysis, but technical details aimed at the specialist statisticianare confined to sections which the more general reader can safelyomit.There is an associated web site with MATLAB and S-PLUSimplementations of the methods discussed, together with all the datasets that are not proprietary. Jim Ramsay is Professor of Psychology atMcGill University, and is an international authority on many aspects ofmultivariate analysis. He was elected President of the StatisticalSociety of Canada for the term 2002-3 and is a holder of the Society'sGold Medal for his work in functional data analysis. His statisticalwork draws on his collaborations with researchers in speecharticulation, biomechanics, economics, human biology, meteorology andpsychology. Bernard Silverman is Professor of Statistics at BristolUniversity. He was President of the Institute of Mathematical Statisticsin 2000-1 and has held various offices in the Royal StatisticalSociety. He is a Fellow of the Royal Society and a member of AcademiaEuropaea. His main specialty is computational statistics,and he is theauthor or editor of several highly regarded books in this area. He hasalso published widely in theoretical and applied statistics, and inmany other fields, including law, human and veterinary medicine, earthsciences and engineering.
Table of Contents
Preface v
1 Introduction 1
1.1 Why consider functional data at all? 1
1.2 TheWeb site 2
1.3 The case studies 2
1.4 How is functional data analysis distinctive? 14
1.5 Conclusion and bibliography 15
2 Life Course Data in Criminology 17
2.1 Criminology life course studies 17
2.1.1 Background 17
2.1.2 The life course data 18
2.2 First steps in a functional approach 19
2.2.1 Turning discrete values into a functional datum 19
2.2.2 Estimating the mean 21
2.3 Functional principal component analyses 23
2.3.1 The basic methodology 23
2.3.2 Smoothing the PCA 26
2.3.3 Smoothed PCA of the criminology data 26
2.3.4 Detailed examination of the scores 28
2.4 What have we seen? 31
2.5 How are functions stored and processed? 33
2.5.1 Basis expansions 33
2.5.2 Fitting basis coefficients to the observed data 35
2.5.3 Smoothing the sample mean function 36
2.5.4 Calculations for smoothed functional PCA 37
2.6 Cross-validation for estimating the mean 38
2.7 Notes and bibliography 40
3 The Nondurable Goods Index 41
3.1 Introduction 41
3.2 Transformation and smoothing 43
3.3 Phase-plane plots 44
3.4 The nondurable goods cycles 47
3.5 What have we seen? 54
3.6 Smoothing data for phase-plane plots55
3.6.1 Fourth derivative roughness penalties 55
3.6.2 Choosing the smoothing parameter 55
4 Bone Shapes from a Paleopathology Study 57
4.1 Archaeology and arthritis 57
4.2 Data capture 58
4.3 How are the shapes parameterized? 59
4.4 A functional principal components analysis 61
4.4.1 Procrustes rotation and PCA calculation 61
4.4.2 Visualizing the components of shape variability 61
4.5 Varimax rotation of the principal components 63
4.6 Bone shapes and arthritis: Clinical relationship? 65
4.7 What have we seen? 66
4.8 Notes and bibliography 66
5 Modeling Reaction-Time Distributions 69
5.1 Introduction 69
5.2 Nonparametric modeling of density functions 71
5.3 Estimating density and individual differences 73
5.4 Exploring variation across subjects with PCA 76
5.5 What have we seen? 79
5.6 Technical details 80
6 Zooming in on Human Growth 83
6.1 Introduction 83
6.2 Height measurements at three scales 84
6.3 Velocity and acceleration 86
6.4 An equation for growth 89
6.5 Timing or phase variation in growth 91
6.6 Amplitude and phase variation in growth 93
6.7 What we have seen? 96
6.8 Notes and further issues 97
6.8.1 Bibliography 97
6.8.2 The growth data 98
6.8.3 Estimating a smooth monotone curve to fit data 98
7 Time Warping Handwriting and Weather Records 101
7.1 Introduction 101
7.2 Formulating the registration problem 102
7.3 Registering the printing data 104
7.4 Registering the weather data 105
7.5 What have we seen? 110
7.6 Notes and references 110
7.6.1 Continuous registration 110
7.6.2 Estimation of the warping function 113
8 How Do Bone Shapes Indicate Arthritis? 115
8.1 Introduction 115
8.2 Analyzing shapes without landmarks 116
8.3 Investigating shape variation 120
8.3.1 Looking at means alone 120
8.3.2 Principal components analysis 120
8.4 The shape of arthritic bones 123
8.4.1 Linear discriminant analysis 123
8.4.2 Regularizing the discriminant analysis 125
8.4.3 Why not just look at the group means? 127
8.5 What have we seen? 128
8.6 Notes and further issues 128
8.6.1 Bibliography 128
8.6.2 Why is regularization necessary? 129
8.6.3 Cross-validation in classification problems 130
9 Functional Models for Test Items 131
9.1 Introduction 131
9.2 The ability space curve 132
9.3 Estimating item response functions 135
9.4 PCA of log odds-ratio functions 136
9.5 Do women and men perform differently on this test? 138
9.6 A nonlatent trait: Arc length 140
9.7 What have we seen? 143
9.8 Notes and bibliography 143
10 Predicting Lip Acceleration from Electromyography 145
10.1 The neural control of speech 145
10.2 The lip and EMG curves 147
10.3 The linear model for the data 148
10.4 The estimated regression function 150
10.5 How far back should the historical model go? 152
10.6 What have we seen? 155
10.7 Notes and bibliography 155
11 The Dynamics of Handwriting Printed Characters 157
11.1 Recording handwriting in real time 157
11.2 An introduction to dynamic models 158
11.3 One subject’s printing data 160
11.4 A differential equation for handwriting 162
11.5 Assessing the fit of the equation 165
11.6 Classifying writers by using their dynamic equations 166
11.7 What have we seen? 170
12 A Differential Equation for Juggling 171
12.1 Introduction 171
12.2 The data and preliminary analyses 172
12.3 Features in the average cycle 173
12.4 The linear differential equation 176
12.5 What have we seen? 180
12.6 Notes and references 181
References 183
Index 187
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