Generalized additive models:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
London u.a.
Chapman and Hall
1990
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Monographs on statistics and applied probability
43 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002764186&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XV, 335 S. graph. Darst. |
| ISBN: | 0412343908 |
Internformat
MARC
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| 245 | 1 | 0 | |a Generalized additive models |c T. J. Hastie ; R. J. Tibshirani |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a London u.a. |b Chapman and Hall |c 1990 | |
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| 650 | 4 | |a Regression analysis | |
| 650 | 4 | |a Smoothing (Statistics) | |
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Datensatz im Suchindex
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| adam_text |
Contents
Preface xiii
1 Introduction 1
1.1 What's in this book 1
1.2 A word of caution 6
1.3 How to read this book 6
1.4 Data sets used in this book 6
1.5 Notation 7
2 Smoothing 9
2.1 What is a smoother? 9
2.2 Scatterplot smoothing: definition 13
2.3 Parametric regression 14
2.4 Bin smoothers 14
2.5 Running mean and running line smoothers 15
2.6 Kernel smoothers 18
2.7 Running medians and enhancements 20
2.8 Equivalent kernels 20
2.9 Regression splines 22
2.10 Cubic smoothing splines 27
2.11 Locally weighted running line smoothers 29
2.12 Smoothers for multiple predictors 32
2.13 Bibliographic notes 34
2.14 Further results and exercises 2 35
3 Smoothing in detail 39
3.1 Introduction 39
3.2 A formal model for scatterplot smoothing 39
3.3 The bias variance trade off 40
vii
viii CONTENTS
3.4 Automatic selection of smoothing parameters 42
3.4.1 Cross validation 42
3.4.2 The bias variance trade off for linear smoothers 44
3.4.3 Cross validation for linear smoothers 46
3.4.4 The Cp statistic 48
3.4.5 Variations on cross validation and
a comparison with Cp 49
3.4.6 Discussion 52
3.5 Degrees of freedom of a smoother 52
3.6 A Bayesian model for smoothing 55
3.7 Eigenanalysis of a smoother and spectral smoothing 57
3.8 Variance of a smooth and confidence bands 60
3.8.1 Pointwise standard error bands 60
3.8.2 Global confidence sets 61
3.9 Approximate F tests 65
3.10 Asymptotic behaviour of smoothers 68
3.11 Special topics 70
3.11.1 Nonlinear smoothers 70
3.11.2 Kriging 71
3.11.3 Smoothing and penalized least squares 72
3.11.4 Weighted smoothing 72
3.11.5 Tied predictor values 74
3.11.6 Resistant smoothing 74
3.12 Bibliographical notes 76
3.13 Further results and exercises 3 79
4 Additive models 82
4.1 Introduction 82
4.2 Multiple regression and linear models 82
4.3 Additive models 86
4.4 Fitting additive models 89
4.5 Generalized additive models: logistic regression 95
4.6 Bibliographic notes 102
4.7 Further results and exercises 4 103
5 Some theory for additive models 105
5.1 Introduction 105
5.2 Estimating equations for additive models 106
5.2.1 L2 function spaces 107
5.2.2 Penalized least squares 110
CONTENTS ix
5.2.3 Reproducing kernel Hilbert spaces 112
5.3 Solutions to the estimating equations 114
5.3.1 Introduction 114
5.3.2 Projection smoothers 115
5.3.3 Semi parametric models 118
5.3.4 Backfitting with two smoothers 118
5.3.5 Existence and uniqueness: p smoothers 121
5.3.6 Convergence of backfitting: p smoothers 122
5.3.7 Summary of the main results of the section 123
5.4 Special topics 124
5.4.1 Weighted additive models 124
5.4.2 A modified backfitting algorithm 124
5.4.3 Explicit solutions to the estimating equations 126
5.4.4 Standard errors 127
5.4.5 Degrees of freedom 128
5.4.6 A Bayesian version of additive models 129
5.5 Bibliographic notes 130
5.6 Further results and exercises 5 132
6 Generalized additive models 136
6.1 Introduction 136
6.2 Fisher scoring for generalized linear models 137
6.3 Local scoring for generalized additive models 140
6.4 Illustrations 141
6.4.1 Clotting times of blood 141
6.4.2 Warm cardioplegia 143
6.5 Derivation of the local scoring procedure 148
6.5.1 L2 function spaces 148
6.5.2 Penalized likelihood 149
6.6 Convergence of the local scoring algorithm 151
6.7 Semi parametric generalized linear models 152
6.8 Inference 155
6.8.1 Analysis of deviance 155
6.8.2 Standard error bands 156
6.8.3 Degrees of freedom 157
6.9 Smoothing parameter selection 159
6.10 Overinterpreting additive fits 161
6.11 Missing predictor values 166
6.12 Estimation of the link function 166
x CONTENTS
6.13 Local likelihood estimation 167
6.14 Bibliographic notes 169
6.15 Further results and exercises 6 171
7 Response transformation models 174
7.1 Introduction 174
7.2 The ACE algorithm 175
7.2.1 Introduction 175
7.2.2 ACE in L2 function spaces 179
7.2.3 ACE and penalized least squares 181
7.2.4 Convergence of ACE with linear smoothers 182
7.2.5 A close ancestor to ACE: canonical correlation 183
7.2.6 Some anomalies of ACE 184
7.3 Response transformations for regression 187
7.3.1 Introduction 187
7.3.2 Generalizations of the Box Cox procedure 187
7.3.3 Comparison of generalized Box Cox and ACE 189
7.4 Additivity and variance stabilization 190
7.4.1 Some properties of AVAS 193
7.5 Further topics 194
7.5.1 Prediction from a transformation model 194
7.5.2 Methods for inference 195
7.6 Bibliographical notes 196
7.7 Further results and exercises 7 197
8 Extensions to other settings 201
8.1 Introduction 201
8.2 Matched case control data 202
8.2.1 Background 202
8.2.2 Estimation 203
8.2.3 Maximizing the conditional likelihood
for the linear model 204
8.2.4 Spline estimation for a single function 205
8.2.5 Algorithm for the additive model 207
8.2.6 A simulated example 209
8.3 The proportional hazards model 211
8.3.1 Background 211
8.3.2 Estimation 211
8.3.3 Further details of the computations 213
8.3.4 An example 214
CONTENTS xi
8.4 The proportional odds model 219
8.4.1 Background 219
8.4.2 Fitting the additive model 220
8.4.3 Illustration 223
8.5 Seasonal decomposition of time series 224
8.5.1 The STL procedure 224
8.5.2 Eigen analysis and bandwidth selection 230
8.6 Bibliographic notes 231
8.7 Further results and exercises 8 232
9 Further topics 235
9.1 Introduction 235
9.2 Resistant fitting 236
9.2.1 Resistant fitting of additive models 236
9.2.2 Resistant fitting of generalized additive models 240
9.2.3 Illustration 242
9.2.4 Influence and resistance 244
9.3 Parametric additive models 245
9.3.1 Regression splines 246
9.3.2 Simple knot selection schemes for
regression splines 247
9.3.3 A simulated example 247
9.3.4 Adaptive knot selection strategies 249
9.3.5 Discussion of regression splines 251
9.3.6 Generalized ridge regression — pseudo
additive models 254
9.3.7 Illustration: diagnostics for additive models 256
9.4 Model selection techniques 259
9.4.1 Backward and forward stepwise selection
techniques 260
9.4.2 Adaptive regression splines: TURBO 261
9.4.3 Adaptive backfitting: BRUTO 262
9.5 Modelling interactions 264
9.5.1 Simple interactions 264
9.5.2 Interactions resulting in separate curves 265
9.5.3 Hierarchical models 266
9.5.4 Examining residuals for interactions 268
9.5.5 Illustration 268
9.5.6 Regression trees 271
xii CONTENTS
9.5.7 Multivariate adaptive regression
splines: MARS 275
9.6 Bibliographic notes 277
9.7 Further results and exercises 9 278
10 Case studies 281
10.1 Introduction 281
10.2 Kyphosis in laminectomy patients 282
10.3 Atmospheric ozone concentration 294
Appendices 301
A Data 301
B Degrees of freedom 305
C Software 307
References 311
Author index 325
Subject index 329 |
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV004458805 |
| illustrated | Illustrated |
| indexdate | 2025-01-11T13:44:21Z |
| institution | BVB |
| isbn | 0412343908 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002764186 |
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| physical | XV, 335 S. graph. Darst. |
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| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Hastie, Trevor 1953- Verfasser (DE-588)172128242 aut Generalized additive models T. J. Hastie ; R. J. Tibshirani 1. ed. London u.a. Chapman and Hall 1990 XV, 335 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 43 Analyse de régression Lissage (Statistique) Modèles linéaires (Statistique) Modèles mathématiques ram Statistique mathématique ram Linear models (Statistics) Regression analysis Smoothing (Statistics) Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd rswk-swf Statistisches Modell (DE-588)4121722-6 gnd rswk-swf Lineares Regressionsmodell (DE-588)4127971-2 gnd rswk-swf Verallgemeinertes lineares Modell (DE-588)4124382-1 s DE-188 Lineares Regressionsmodell (DE-588)4127971-2 s Statistisches Modell (DE-588)4121722-6 s 1\p DE-604 Tibshirani, Robert 1956- Verfasser (DE-588)172417740 aut Monographs on statistics and applied probability 43 (DE-604)BV002494005 43 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002764186&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hastie, Trevor 1953- Tibshirani, Robert 1956- Generalized additive models Monographs on statistics and applied probability Analyse de régression Lissage (Statistique) Modèles linéaires (Statistique) Modèles mathématiques ram Statistique mathématique ram Linear models (Statistics) Regression analysis Smoothing (Statistics) Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Statistisches Modell (DE-588)4121722-6 gnd Lineares Regressionsmodell (DE-588)4127971-2 gnd |
| subject_GND | (DE-588)4124382-1 (DE-588)4121722-6 (DE-588)4127971-2 |
| title | Generalized additive models |
| title_auth | Generalized additive models |
| title_exact_search | Generalized additive models |
| title_full | Generalized additive models T. J. Hastie ; R. J. Tibshirani |
| title_fullStr | Generalized additive models T. J. Hastie ; R. J. Tibshirani |
| title_full_unstemmed | Generalized additive models T. J. Hastie ; R. J. Tibshirani |
| title_short | Generalized additive models |
| title_sort | generalized additive models |
| topic | Analyse de régression Lissage (Statistique) Modèles linéaires (Statistique) Modèles mathématiques ram Statistique mathématique ram Linear models (Statistics) Regression analysis Smoothing (Statistics) Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Statistisches Modell (DE-588)4121722-6 gnd Lineares Regressionsmodell (DE-588)4127971-2 gnd |
| topic_facet | Analyse de régression Lissage (Statistique) Modèles linéaires (Statistique) Modèles mathématiques Statistique mathématique Linear models (Statistics) Regression analysis Smoothing (Statistics) Verallgemeinertes lineares Modell Statistisches Modell Lineares Regressionsmodell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002764186&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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