Local polynomial modelling and its applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Chapman & Hall
1996
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Monographs on statistics and applied probability
66 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 341 S. Ill., graph. Darst. |
| ISBN: | 0412983214 |
Internformat
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Datensatz im Suchindex
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Contents
Preface xiii
1 Introduction 1
1.1 From linear regression to nonlinear regression 1
1.2 Local modelling 4
1.3 Bandwidth selection and model complexity 7
1.4 Scope of the book 9
1.5 Implementation of nonparametric techniques 11
1.6 Further reading 12
2 Overview of existing methods 13
2.1 Introduction 13
2.2 Kernel estimators 14
2.2.1 Nadaraya Watson estimator 14
2.2.2 Gasser Muller estimator 15
2.2.3 Limitations of a local constant fit 17
2.3 Local polynomial fitting and derivative estimation 18
2.3.1 Local polynomial fitting 19
2.3.2 Derivative estimation 22
2.4 Locally weighted scatter plot smoothing 22
2.4.1 Robust locally weighted regression 24
2.4.2 An example 26
2.5 Wavelet thresholding 27
2.5.1 Orthogonal series based methods 28
2.5.2 Basic ingredient of multiresolution analysis 31
2.5.3 Wavelet shrinkage estimator 34
2.5.4 Discrete wavelet transform 35
2.6 Spline smoothing 39
2.6.1 Polynomial spline 40
2.6.2 Smoothing spline 43
viii CONTENTS
2.7 Density estimation 46
2.7.1 Kernel density estimation 46
2.7.2 Regression view of density estimation 50
2.7.3 Wavelet estimators 52
2.7.4 Logspline method 54
2.8 Bibliographic notes 55
3 Framework for local polynomial regression 57
3.1 Introduction 57
3.2 Advantages of local polynomial fitting 60
3.2.1 Bias and variance 61
3.2.2 Equivalent kernels 63
3.2.3 Ideal choice of bandwidth 66
3.2.4 Design adaptation property 68
3.2.5 Automatic boundary carpentry 69
3.2.6 Universal optimal weighting scheme 74
3.3 Which order of polynomial fit to use? 76
3.3.1 Increases of variability 77
3.3.2 It is an odd world 79
3.3.3 Variable order approximation 80
3.4 Best linear smoothers 84
3.4.1 Best linear smoother at interior: optimal
rates and constants 84
3.4.2 Best linear smoother at boundary 89
3.5 Minimax efficiency of local polynomial fitting 91
3.5.1 Modulus of continuity 92
3.5.2 Best rates and nearly best constant 94
3.6 Fast computing algorithms 94
3.6.1 Binning implementation 96
3.6.2 Updating algorithm 99
3.7 Complements 100
3.8 Bibliographic notes 105
4 Automatic determination of model complexity 109
4.1 Introduction 109
4.2 Rule of thumb for bandwidth selection 110
4.3 Estimated bias and variance 113
4.4 Confidence intervals 116
4.5 Residual squares criterion 118
4.5.1 Residual squares criterion 118
4.5.2 Constant bandwidth selection 119
4.5.3 Variable bandwidth selection 122
CONTENTS ix
4.5.4 Computation and related issues 122
4.6 Refined bandwidth selection 123
4.6.1 Improving rates of convergence 123
4.6.2 Constant bandwidth selection 123
4.6.3 Variable bandwidth selection 124
4.7 Variable bandwidth and spatial adaptation 128
4.7.1 Qualification of spatial adaptation 128
4.7.2 Comparison with wavelets 129
4.8 Smoothing techniques in use 132
4.8.1 Example 1: modelling and model diagnostics 133
4.8.2 Example 2: comparing two treatments 136
4.8.3 Example 3: analyzing a longitudinal data set 137
4.9 A blueprint for local modelling 141
4.10 Other existing methods 148
4.10.1 Normal reference method 149
4.10.2 Cross validation 149
4.10.3 Nearest neighbor bandwidth 151
4.10.4 Plug in ideas 152
4.10.5 Sheather and Jones' bandwidth selector 153
4.11 Complements 154
4.12 Bibliographic notes 157
5 Applications of local polynomial modelling 159
5.1 Introduction 159
5.2 Censored regression 160
5.2.1 Preliminaries 160
5.2.2 Censoring unbiased transformation 165
5.2.3 Local polynomial regression 170
5.2.4 An asymptotic result 173
5.3 Proportional hazards model 175
5.3.1 Partial likelihood 175
5.3.2 Local partial likelihood 179
5.3.3 Determining model complexity 183
5.3.4 Complete likelihood 187
5.4 Generalized linear models 189
5.4.1 Exponential family models 190
5.4.2 Quasi likelihood and deviance residuals 193
5.4.3 Local quasi likelihood 194
5.4.4 Bias and variance 196
5.4.5 Bandwidth selection 197
5.5 Robust regression 199
5.5.1 Robust methods 199
x CONTENTS
5.5.2 Quantile regression 201
5.5.3 Simultaneous estimation of location and
scale functions 207
5.6 Complements 208
5.7 Bibliographic notes 214
6 Applications in nonlinear time series 217
6.1 Introduction 217
6.2 Nonlinear prediction 218
6.2.1 Mixing conditions 218
6.2.2 Local polynomial fitting 220
6.2.3 Estimation of conditional densities 224
6.3 Percentile and expectile regression 228
6.3.1 Regression percentile 229
6.3.2 Expectile regression 230
6.4 Spectral density estimation 233
6.4.1 Smoothed log periodogram 235
6.4.2 Maximum local likelihood method 237
6.4.3 Smoothed periodogram 242
6.5 Sensitivity measures and nonlinear prediction 243
6.5.1 Sensitivity measures 244
6.5.2 Noise amplification 247
6.5.3 Nonlinear prediction error 247
6.6 Complements 249
6.7 Bibliographic notes 260
7 Local polynomial regression for multivariate data 263
7.1 Introduction 263
7.2 Generalized additive models 265
7.3 Generalized partially linear single index models 272
7.3.1 Partially linear models 273
7.3.2 Single index models 274
7.3.3 Generalized partially linear single index models276
7.4 Modelling interactions 283
7.4.1 Interactions in generalized additive models 283
7.4.2 Interactions in generalized partially linear
single index models 287
7.4.3 Multivariate adaptive regression splines 289
7.5 Sliced inverse regression 290
7.6 Local polynomial regression as a building block 295
7.7 Robustness 296
7.8 Local linear regression in the multivariate setting 297
CONTENTS xi
7.8.1 Multivariate local linear regression estimator 297
7.8.2 Bias and variance 301
7.8.3 Optimal weight function 302
7.8.4 Efficiency 303
7.9 Bibliographic notes 304
References 307
Author index 330
Subject index 336 |
| any_adam_object | 1 |
| author | Fan, Jianqing Gijbels, Irène |
| author_GND | (DE-588)120683989 |
| author_facet | Fan, Jianqing Gijbels, Irène |
| author_role | aut aut |
| author_sort | Fan, Jianqing |
| author_variant | j f jf i g ig |
| building | Verbundindex |
| bvnumber | BV010950227 |
| callnumber-first | Q - Science |
| callnumber-label | QA278 |
| callnumber-raw | QA278.2.F36 1996 |
| callnumber-search | QA278.2.F36 1996 |
| callnumber-sort | QA 3278.2 F36 41996 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 840 |
| ctrlnum | (OCoLC)34917116 (DE-599)BVBBV010950227 |
| dewey-full | 512.942 519.5/36 519.5/3621 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 519 - Probabilities and applied mathematics |
| dewey-raw | 512.942 519.5/36 519.5/36 21 |
| dewey-search | 512.942 519.5/36 519.5/36 21 |
| dewey-sort | 3512.942 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV010950227 |
| illustrated | Illustrated |
| indexdate | 2024-12-06T09:03:22Z |
| institution | BVB |
| isbn | 0412983214 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007324056 |
| oclc_num | 34917116 |
| open_access_boolean | |
| owner | DE-739 DE-824 DE-521 |
| owner_facet | DE-739 DE-824 DE-521 |
| physical | XV, 341 S. Ill., graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Chapman & Hall |
| record_format | marc |
| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Fan, Jianqing Verfasser aut Local polynomial modelling and its applications J. Fan and I. Gijbels 1. ed. London [u.a.] Chapman & Hall 1996 XV, 341 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 66 Analyse de régression Analyse de régression ram Regressieanalyse gtt Statistiek gtt Statistik Regression analysis Nonparametric statistics Nichtparametrisches Verfahren (DE-588)4339273-8 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Statistisches Modell (DE-588)4121722-6 gnd rswk-swf Polynomiale Regression (DE-588)4221406-3 gnd rswk-swf Polynomiale Regression (DE-588)4221406-3 s Nichtparametrisches Verfahren (DE-588)4339273-8 s DE-604 Regressionsanalyse (DE-588)4129903-6 s Datenanalyse (DE-588)4123037-1 s 1\p DE-604 Statistisches Modell (DE-588)4121722-6 s 2\p DE-604 Gijbels, Irène Verfasser (DE-588)120683989 aut Monographs on statistics and applied probability 66 (DE-604)BV002494005 66 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007324056&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fan, Jianqing Gijbels, Irène Local polynomial modelling and its applications Monographs on statistics and applied probability Analyse de régression Analyse de régression ram Regressieanalyse gtt Statistiek gtt Statistik Regression analysis Nonparametric statistics Nichtparametrisches Verfahren (DE-588)4339273-8 gnd Regressionsanalyse (DE-588)4129903-6 gnd Datenanalyse (DE-588)4123037-1 gnd Statistisches Modell (DE-588)4121722-6 gnd Polynomiale Regression (DE-588)4221406-3 gnd |
| subject_GND | (DE-588)4339273-8 (DE-588)4129903-6 (DE-588)4123037-1 (DE-588)4121722-6 (DE-588)4221406-3 |
| title | Local polynomial modelling and its applications |
| title_auth | Local polynomial modelling and its applications |
| title_exact_search | Local polynomial modelling and its applications |
| title_full | Local polynomial modelling and its applications J. Fan and I. Gijbels |
| title_fullStr | Local polynomial modelling and its applications J. Fan and I. Gijbels |
| title_full_unstemmed | Local polynomial modelling and its applications J. Fan and I. Gijbels |
| title_short | Local polynomial modelling and its applications |
| title_sort | local polynomial modelling and its applications |
| topic | Analyse de régression Analyse de régression ram Regressieanalyse gtt Statistiek gtt Statistik Regression analysis Nonparametric statistics Nichtparametrisches Verfahren (DE-588)4339273-8 gnd Regressionsanalyse (DE-588)4129903-6 gnd Datenanalyse (DE-588)4123037-1 gnd Statistisches Modell (DE-588)4121722-6 gnd Polynomiale Regression (DE-588)4221406-3 gnd |
| topic_facet | Analyse de régression Regressieanalyse Statistiek Statistik Regression analysis Nonparametric statistics Nichtparametrisches Verfahren Regressionsanalyse Datenanalyse Statistisches Modell Polynomiale Regression |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007324056&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT fanjianqing localpolynomialmodellinganditsapplications AT gijbelsirene localpolynomialmodellinganditsapplications |