Partially linear models:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Heidelberg ; New York
Physica-Verl.
2000
|
| Schriftenreihe: | Contributions to statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | X, 202 S. |
| ISBN: | 3790813001 |
Internformat
MARC
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| 100 | 1 | |a Härdle, Wolfgang |d 1953- |e Verfasser |0 (DE-588)110357116 |4 aut | |
| 245 | 1 | 0 | |a Partially linear models |c Wolfgang Härdle ; Hua Liang ; Jiti Gao |
| 264 | 1 | |a Heidelberg ; New York |b Physica-Verl. |c 2000 | |
| 300 | |a X, 202 S. | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Contributions to statistics | |
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| 700 | 1 | |a Gao, Jiti |d 1962- |e Verfasser |0 (DE-588)122189892 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009054124 | ||
Datensatz im Suchindex
| _version_ | 1804128047689891840 |
|---|---|
| adam_text | CONTENTS
PREFACE
...................................
v
1
INTRODUCTION
............................ 1
1.1
Background, History and Practical Examples
............ 1
1.2
The Least Squares Estimators
.................... 12
1.3
Assumptions and Remarks
...................... 14
1.4
The Scope of the Monograph
..................... 16
1.5
The Structure of the Monograph
................... 17
2
ESTIMATION OF THE PARAMETRIC COMPONENT
... 19
2.1
Estimation with Heteroscedastic Errors
............... 19
2.1.1
Introduction
.......................... 19
2.1.2
Estimation of the Non-constant Variance Functions
.... 22
2.1.3
Selection of Smoothing Parameters
............. 26
2.1.4
Simulation Comparisons
................... 27
2.1.5
Technical Details
....................... 28
2.2
Estimation with Censored Data
................... 32
2.2.1
Introduction
.......................... 32
2.2.2
Synthetic Data and Statement of the Main Results
.... 33
2.2.3
Estimation of the Asymptotic Variance
........... 36
2.2.4
A Numerical Example
.................... 37
2.2.5
Technical Details
....................... 38
2.3
Bootstrap Approximations
...................... 40
2.3.1
Introduction
.......................... 40
2.3.2
Bootstrap Approximations
.................. 41
2.3.3
Numerical Results
...................... 43
3
ESTIMATION OF THE NONPARAMETRIC COMPONENT
45
3.1
Introduction
.............................. 45
viii CONTENTS
3.2
Consistency Results
.......................... 46
3.3
Asymptotic Normality
........................ 49
3.4
Simulated and Real Examples
.................... 50
3.5
Appendix
............................... 52
4
ESTIMATION WITH MEASUREMENT ERRORS
...... 55
4.1
Linear Variables with Measurement Errors
............. 55
4.1.1
Introduction and Motivation
................. 55
4.1.2
Asymptotic Normality for the Parameters
......... 56
4.1.3
Asymptotic Results for the Nonparametric Part
...... 58
4.1.4
Estimation of Error Variance
................ 58
4.1.5
Numerical Example
...................... 59
4.1.6
Discussions
.......................... 61
4.1.7
Technical Details
....................... 61
4.2
Nonlinear Variables with Measurement Errors
........... 65
4.2.1
Introduction
.......................... 65
4.2.2
Construction of Estimators
.................. 66
4.2.3
Asymptotic Normality
.................... 67
4.2.4
Simulation Investigations
................... 68
4.2.5
Technical Details
....................... 70
5
SOME RELATED THEORETIC TOPICS
............. 77
5.1
The Laws of the Iterated Logarithm
................. 77
5.1.1
Introduction
.......................... 77
5.1.2
Preliminary Processes
.................... 78
5.1.3
Appendix
........................... 79
5.2
The Berry-Esseen Bounds
...................... 82
5.2.1
Introduction and Results
................... 82
5.2.2
Basic Facts
.......................... 83
5.2.3
Technical Details
....................... 87
5.3
Asymptotically Efficient Estimation
................. 94
5.3.1
Motivation
........................... 94
5.3.2
Construction of Asymptotically Efficient Estimators
.... 94
5.3.3
Four Lemmas
......................... 97
CONTENTS ix
5.3.4 Appendix........................... 99
5.4
Bahadur Asymptotic Efficiency
................... 104
5.4.1
Definition
........................... 104
5.4.2
Tail Probability
........................ 105
5.4.3
Technical Details
....................... 106
5.5
Second Order Asymptotic Efficiency
.................
Ill
5.5.1
Asymptotic Efficiency
....................
Ill
5.5.2
Asymptotic Distribution Bounds
.............. 113
5.5.3
Construction of
2nd
Order Asymptotic Efficient Estimator
117
5.6
Estimation of the Error Distribution
................ 119
5.6.1
Introduction
.......................... 119
5.6.2
Consistency Results
...................... 120
5.6.3
Convergence Rates
...................... 124
5.6.4
Asymptotic Normality and
LIL
............... 125
6
PARTIALLY LINEAR TIME SERIES MODELS
........ 127
6.1
Introduction
.............................. 127
6.2
Adaptive Parametric and Nonparametrie Tests
........... 127
6.2.1
Asymptotic Distributions of Test Statistics
......... 127
6.2.2
Power Investigations of the Test Statistics
......... 131
6.3
Optimum Linear Subset Selection
.................. 135
6.3.1
A Consistent
CV
Criterion
.................. 136
6.3.2
Simulated and Real Examples
................ 139
6.4
Optimum Bandwidth Selection
................... 144
6.4.1
Asymptotic Theory
...................... 144
6.4.2
Computational Aspects
.................... 149
6.5
Other Related Developments
..................... 156
6.6
The Assumptions and the Proofs of Theorems
........... 157
6.6.1
Mathematical Assumptions
................. 157
6.6.2
Technical Details
....................... 160
APPENDIX: BASIC LEMMAS
..................... 181
AUTHOR INDEX
.............................. 197
χ
CONTENTS
SUBJECT INDEX
.............................201
SYMBOLS AND NOTATION
......................203
In the last ten years, there has been increasing
interest and activity in the general area of par¬
tially linear regression smoothing in statistics.
Many methods and techniques have been pro¬
posed and studies. This monograph hopes to
bring an up-to-date presentation of the state of
the art of partially linear regression techniques.
The emphasis is on methodologies rather than
on the theory, with a particular focus on applica¬
tions of partially linear regression techniques to
various statistical problems. These problems
include least squares regression, asymptotically
efficient estimation, bootstrap resampling, cen¬
sored data analysis, linear measurement error
models, nonlinear measurement models, non¬
linear and nonparametric time series models.
|
| any_adam_object | 1 |
| author | Härdle, Wolfgang 1953- Liang, Hua 1965- Gao, Jiti 1962- |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV013279653 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:43:02Z |
| institution | BVB |
| isbn | 3790813001 |
| language | English |
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| physical | X, 202 S. |
| publishDate | 2000 |
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| publisher | Physica-Verl. |
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| series2 | Contributions to statistics |
| spelling | Härdle, Wolfgang 1953- Verfasser (DE-588)110357116 aut Partially linear models Wolfgang Härdle ; Hua Liang ; Jiti Gao Heidelberg ; New York Physica-Verl. 2000 X, 202 S. txt rdacontent n rdamedia nc rdacarrier Contributions to statistics Regressieanalyse gtt Statistiek gtt Statistik Linear models (Statistics) Partielles lineares Modell (DE-588)4624309-4 gnd rswk-swf Partielles lineares Modell (DE-588)4624309-4 s DE-604 Liang, Hua 1965- Verfasser (DE-588)122189841 aut Gao, Jiti 1962- Verfasser (DE-588)122189892 aut Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009054124&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009054124&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Härdle, Wolfgang 1953- Liang, Hua 1965- Gao, Jiti 1962- Partially linear models Regressieanalyse gtt Statistiek gtt Statistik Linear models (Statistics) Partielles lineares Modell (DE-588)4624309-4 gnd |
| subject_GND | (DE-588)4624309-4 |
| title | Partially linear models |
| title_auth | Partially linear models |
| title_exact_search | Partially linear models |
| title_full | Partially linear models Wolfgang Härdle ; Hua Liang ; Jiti Gao |
| title_fullStr | Partially linear models Wolfgang Härdle ; Hua Liang ; Jiti Gao |
| title_full_unstemmed | Partially linear models Wolfgang Härdle ; Hua Liang ; Jiti Gao |
| title_short | Partially linear models |
| title_sort | partially linear models |
| topic | Regressieanalyse gtt Statistiek gtt Statistik Linear models (Statistics) Partielles lineares Modell (DE-588)4624309-4 gnd |
| topic_facet | Regressieanalyse Statistiek Statistik Linear models (Statistics) Partielles lineares Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009054124&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=009054124&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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