Local polynomial modelling and its applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2003
|
| Ausgabe: | 1. CRC Press repr. |
| Schriftenreihe: | Monographs on statistics and applied probability
66 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XV, 341 S. graph. Darst. |
| ISBN: | 0412983214 9780412983214 |
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Datensatz im Suchindex
| _version_ | 1813706113568210944 |
|---|---|
| adam_text |
Contents
Preface
xiii
1
Introduction
1
1.1
Prom
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-Müller
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
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
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
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
Percentik
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
Monographs on Statistics and Applied Probability
66
Local Polynomial Modelling and Its Applications J. Fan
and I. Gijbels
Data-analytic approaches to regression problems, arising from
many scientific disciplines, are described in this book. The aim
of these nonparametric methods is to relax assumptions on
the form of a regression function, and to let data search for a
suitable function that describes the data well. The use of these
nonparametric functions with parametric techniques can yield
very powerful data analysis tools.
Local Polynomial Modelling and Its Applications provides
an up-to-date picture on state-of-the-art nonparametric
regression techniques. The emphasis of the book is on
methodologies rather than on theory, with a particular focus
on applications of nonparametric techniques to various statistical
problems. High-dimensional data-analytic tools are presented,
and the book includes a variety of examples.
This will be a valuable reference for research and applied statis¬
ticians, and will serve as a textbook for graduate students and
others interested in nonparametric regression.
Jianging Fan is Associate Professor in the Department of
Statistics at the University of North Carolina at Chapel Hill,
USA. Irène
Gijbels is Associate Professor in the Institute of
Statistics at the Catholic University of Louvain, Belgium.
A complete list of titles in this series appears at the front of
the book.
Chapman
&
Hall/CRC
Taylor
&
Francis Group
an
informa
business
www.taylorandfrancisgroup.com
6000
Broken Sound Parkway, NW
Suite
300,
Boca Raton, Fl
33487
270
Madison Avenue
Ncv York, NY
1Ο0Ί
6
2
Parit
Square, Milton Parti
Abingdon, Oxon
0X14
4RN, UK
ISBN
о-чів-чвзаі-ч
90000 |
| any_adam_object | 1 |
| author | Fan, Jianqing Gijbels, Irène |
| author_GND | (DE-588)17090492X (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 | BV025503931 |
| classification_rvk | SK 840 |
| classification_tum | MAT 628f |
| ctrlnum | (OCoLC)836958324 (DE-599)BVBBV025503931 |
| discipline | Mathematik |
| edition | 1. CRC Press repr. |
| format | Book |
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| id | DE-604.BV025503931 |
| illustrated | Illustrated |
| indexdate | 2024-10-23T12:02:17Z |
| institution | BVB |
| isbn | 0412983214 9780412983214 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020115104 |
| oclc_num | 836958324 |
| open_access_boolean | |
| owner | DE-11 DE-703 DE-91G DE-BY-TUM DE-384 |
| owner_facet | DE-11 DE-703 DE-91G DE-BY-TUM DE-384 |
| physical | XV, 341 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Fan, Jianqing Verfasser (DE-588)17090492X aut Local polynomial modelling and its applications J. Fan and I. Gijbels 1. CRC Press repr. Boca Raton [u.a.] Chapman & Hall/CRC 2003 XV, 341 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 66 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 Regressionsanalyse (DE-588)4129903-6 s Statistisches Modell (DE-588)4121722-6 s DE-604 Nichtparametrisches Verfahren (DE-588)4339273-8 s Datenanalyse (DE-588)4123037-1 s 1\p DE-604 Polynomiale Regression (DE-588)4221406-3 s 2\p DE-604 Gijbels, Irène Verfasser (DE-588)120683989 aut Monographs on statistics and applied probability 66 (DE-604)BV002494005 66 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020115104&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020115104&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 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 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 | 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 | 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=020115104&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020115104&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT fanjianqing localpolynomialmodellinganditsapplications AT gijbelsirene localpolynomialmodellinganditsapplications |