Spline smoothing and nonparametric regression:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1988
|
| Edition: | 1. print. |
| Series: | Statistics
90 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 438 S. graph. Darst. |
| ISBN: | 0824778693 |
Staff View
MARC
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| 264 | 1 | |a New York [u.a.] |b Dekker |c 1988 | |
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| 650 | 4 | |a Nonparametric statistics | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
PREFACE V
NOTATION xv
1. INTRODUCTION 1
1.1 Regression Analysis 1
1.2 Nonparametric Regression 6
1.3 Scope 11
2. WHAT IS A GOOD ESTIMATOR? 15
2.1 Performance Criteria 15
2.2 Estimating P(A) and R(X) 23
2.3 Other Properties of CV and GCV 35
2.4 Other Criteria 38
Exercises 41
3. FUNCTION SPACES AND SERIES ESTIMATORS 49
3.1 Introduction 49
3.2 Some Function Space Theory 51
3.3 Generalized Fourier Series Estimators 58
3.4 Classical Fourier Series Estimators 64
3.4.1 Form of the Estimator 65
3.4.2 Some Asymptotic Theory 69
3.4.3 Selection of A 76
3.4.4 Asymptotic Distribution Theory 76
3.4.5 An Example 82
3.5 Polynomial Regression 89
3.5.1 Form of the Estimator 92
3.5.2 Some Asymptotic Theory 94
3.5.3 An Example 100
Exercises 101
4. KERNEL ESTIMATORS 109
4.1 Introduction 109
4.2 Kernel Estimators 110
4.3 Asymptotic Theory 124
4.4 Selecting a Kernel 136
4.5 Selection of X 139
xi
xii Contents
4.6 Asymptotic Distribution Theory 144
4.7 Higher Order Kernels, Variable Bandwidths and
Optimal Design 149
4.8 Estimation of Derivatives 155
4.9 Applications 159
4.10 Random t s 167
4.11 Robust Smoothers 173
Exercises 176
5. SMOOTHING SPLINES 189
5.1 Introduction 189
5.2 Smoothing Splines and Polynomial Regression 191
5.3 Derivation and Computation of the Estimator 195
5.3.1 Splines and Natural Splines 196
5.3.2 Form of the Estimator 200
5.3.3 Selecting a Basis 207
5.4 Selecting X and m 220
5.5 Bayesian Interpretations and Inference 233
5.5.1 Bayesian Polynomial Regression 233
5.5.2 Selection of X in the Bayes Model 242
5.5.3 Estimation of a2 and a2 248
5.5.4 Interval Estimation S 250
5.5.5 Diagnostic Analysis 258
Exercises 268
6. SMOOTHING SPLINES: EXTENSIONS AND ASYMPTOTIC THEORY 275
6.1 Introduction 275
6.2 Extensions 276
6.2.1 The Method of Regularization 276
6.2.2 Constraints 283
6.2.3 Multivariate Smoothing Splines 286
6.2.4 Partial Splines 292
6.2.5 Robust Smoothing Splines 294
6.2.6 The Penalty Function Method 295
6.3 Asymptotic Theory 298
6.3.1 Periodic Smoothing Splines 299
6.3.2 The General Case 314
6.3.3 Asymptotics for Smoothing Spline Variants 328
6.4 Applications 331
6.4.1 Estimation of Posterior Probabilities 331
6.4.2 Estimation of Tumor Size Distributions 334
6.4.3 The Stack Loss Data Revisited 338
6.4.4 Other Applications 348
Exercises 348
7. LEAST SQDARES SPLINES AND OTHER ESTIMATORS 353
7.1 Introduction 353
7.2 Least Squares Splines 354
7.2.1 Selecting X 357
Contents xiii
7.2.2 Computational Considerations 363
7.2.3 Extensions 367
7.2.4 Asymptotic Analysis 373
7.2.5 Other Inference Problems 376
7.3 Speckman s Minimax Estimator 378
7.4 Nearest Neighbor Estimators 384
7.5 Additive Nonparametric Regression 387
Exercises 395
APPENDIX: LINEAR AND NONLINEAR REGRESSION 399
A.I Linear Models 399
A.1.1 Parameter Estimation 400
A.1.2 Hypothesis Tests/Interval Estimates 403
A.1.3 Diagnostic Analysis 404
A.2 Nonlinear Models 407
A.2.1 Parameter Estimation 407
A.2.2 Hypothesis Tests/Interval Estimates 411
A.2.3 Diagnostic Analysis 412
REFERENCES 415
INDEX 435
|
| adam_txt |
Contents
PREFACE V
NOTATION xv
1. INTRODUCTION 1
1.1 Regression Analysis 1
1.2 Nonparametric Regression 6
1.3 Scope 11
2. WHAT IS A GOOD ESTIMATOR? 15
2.1 Performance Criteria 15
2.2 Estimating P(A) and R(X) 23
2.3 Other Properties of CV and GCV 35
2.4 Other Criteria 38
Exercises 41
3. FUNCTION SPACES AND SERIES ESTIMATORS 49
3.1 Introduction 49
3.2 Some Function Space Theory 51
3.3 Generalized Fourier Series Estimators 58
3.4 Classical Fourier Series Estimators 64
3.4.1 Form of the Estimator 65
3.4.2 Some Asymptotic Theory 69
3.4.3 Selection of A 76
3.4.4 Asymptotic Distribution Theory 76
3.4.5 An Example 82
3.5 Polynomial Regression 89
3.5.1 Form of the Estimator 92
3.5.2 Some Asymptotic Theory 94
3.5.3 An Example 100
Exercises 101
4. KERNEL ESTIMATORS 109
4.1 Introduction 109
4.2 Kernel Estimators 110
4.3 Asymptotic Theory 124
4.4 Selecting a Kernel 136
4.5 Selection of X 139
xi
xii Contents
4.6 Asymptotic Distribution Theory 144
4.7 Higher Order Kernels, Variable Bandwidths and
Optimal Design 149
4.8 Estimation of Derivatives 155
4.9 Applications 159
4.10 Random t's 167
4.11 Robust Smoothers 173
Exercises 176
5. SMOOTHING SPLINES 189
5.1 Introduction 189
5.2 Smoothing Splines and Polynomial Regression 191
5.3 Derivation and Computation of the Estimator 195
5.3.1 Splines and Natural Splines 196
5.3.2 Form of the Estimator 200
5.3.3 Selecting a Basis 207
5.4 Selecting X and m 220
5.5 Bayesian Interpretations and Inference 233
5.5.1 Bayesian Polynomial Regression 233
5.5.2 Selection of X in the Bayes Model 242
5.5.3 Estimation of a2 and a2 248
5.5.4 Interval Estimation S 250
5.5.5 Diagnostic Analysis 258
Exercises 268
6. SMOOTHING SPLINES: EXTENSIONS AND ASYMPTOTIC THEORY 275
6.1 Introduction 275
6.2 Extensions 276
6.2.1 The Method of Regularization 276
6.2.2 Constraints 283
6.2.3 Multivariate Smoothing Splines 286
6.2.4 Partial Splines 292
6.2.5 Robust Smoothing Splines 294
6.2.6 The Penalty Function Method 295
6.3 Asymptotic Theory 298
6.3.1 Periodic Smoothing Splines 299
6.3.2 The General Case 314
6.3.3 Asymptotics for Smoothing Spline Variants 328
6.4 Applications 331
6.4.1 Estimation of Posterior Probabilities 331
6.4.2 Estimation of Tumor Size Distributions 334
6.4.3 The Stack Loss Data Revisited 338
6.4.4 Other Applications 348
Exercises 348
7. LEAST SQDARES SPLINES AND OTHER ESTIMATORS 353
7.1 Introduction 353
7.2 Least Squares Splines 354
7.2.1 Selecting X 357
Contents xiii
7.2.2 Computational Considerations 363
7.2.3 Extensions 367
7.2.4 Asymptotic Analysis 373
7.2.5 Other Inference Problems 376
7.3 Speckman's Minimax Estimator 378
7.4 Nearest Neighbor Estimators 384
7.5 Additive Nonparametric Regression 387
Exercises 395
APPENDIX: LINEAR AND NONLINEAR REGRESSION 399
A.I Linear Models 399
A.1.1 Parameter Estimation 400
A.1.2 Hypothesis Tests/Interval Estimates 403
A.1.3 Diagnostic Analysis 404
A.2 Nonlinear Models 407
A.2.1 Parameter Estimation 407
A.2.2 Hypothesis Tests/Interval Estimates 411
A.2.3 Diagnostic Analysis 412
REFERENCES 415
INDEX 435 |
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| institution | BVB |
| isbn | 0824778693 |
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| physical | XVII, 438 S. graph. Darst. |
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| spelling | Eubank, Randall L. 1952- Verfasser (DE-588)132752220 aut Spline smoothing and nonparametric regression 1. print. New York [u.a.] Dekker 1988 XVII, 438 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics 90 Analyse de régression Splines, Théorie des Statistique non-paramétrique Nonparametric statistics Regression analysis Spline theory Spline-Approximation (DE-588)4182394-1 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Nichtparametrische Statistik (DE-588)4226777-8 gnd rswk-swf Spline-Funktion (DE-588)4056332-7 gnd rswk-swf Spline-Funktion (DE-588)4056332-7 s DE-604 Nichtparametrische Statistik (DE-588)4226777-8 s Regressionsanalyse (DE-588)4129903-6 s Spline-Approximation (DE-588)4182394-1 s 1\p DE-604 Statistics 90 (DE-604)BV000003265 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015371580&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 | Eubank, Randall L. 1952- Spline smoothing and nonparametric regression Statistics Analyse de régression Splines, Théorie des Statistique non-paramétrique Nonparametric statistics Regression analysis Spline theory Spline-Approximation (DE-588)4182394-1 gnd Regressionsanalyse (DE-588)4129903-6 gnd Nichtparametrische Statistik (DE-588)4226777-8 gnd Spline-Funktion (DE-588)4056332-7 gnd |
| subject_GND | (DE-588)4182394-1 (DE-588)4129903-6 (DE-588)4226777-8 (DE-588)4056332-7 |
| title | Spline smoothing and nonparametric regression |
| title_auth | Spline smoothing and nonparametric regression |
| title_exact_search | Spline smoothing and nonparametric regression |
| title_exact_search_txtP | Spline smoothing and nonparametric regression |
| title_full | Spline smoothing and nonparametric regression |
| title_fullStr | Spline smoothing and nonparametric regression |
| title_full_unstemmed | Spline smoothing and nonparametric regression |
| title_short | Spline smoothing and nonparametric regression |
| title_sort | spline smoothing and nonparametric regression |
| topic | Analyse de régression Splines, Théorie des Statistique non-paramétrique Nonparametric statistics Regression analysis Spline theory Spline-Approximation (DE-588)4182394-1 gnd Regressionsanalyse (DE-588)4129903-6 gnd Nichtparametrische Statistik (DE-588)4226777-8 gnd Spline-Funktion (DE-588)4056332-7 gnd |
| topic_facet | Analyse de régression Splines, Théorie des Statistique non-paramétrique Nonparametric statistics Regression analysis Spline theory Spline-Approximation Regressionsanalyse Nichtparametrische Statistik Spline-Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015371580&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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