Applied nonparametric regression:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge <<[u.a.]>>
Univ. Pr.
1993
|
| Edition: | Repr. |
| Series: | Econometric society monographs
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 333 S. graph. Darst. |
| ISBN: | 0521382483 |
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Record in the Search Index
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| adam_text | Titel: Applied nonparametric regression
Autor: Härdle, Wolfgang
Jahr: 1993
Contents
rrefact page xi
Symbols and notation xiv
PART I. Regression smoothing
Chapter 1. Introduction 3
1.1 Motivation 6
1.2 Scope of this book 12
Chapter 2. Basic idea of smoothing 14
2.1 The stochastic nature of the observations 21
2.2 Hurdles for the smoothing process 22
Complements 23
Chapter 3. Smoothing techniques 24
3.1 Kernel smoothing 24
Kernel estimators axe local polynomial fits 30
Kernel estimators of derivatives 32
Computational aspects of kernel smoothing 35
Exercises 37
Complements 39
Proof of Proposition 3.1.1 39
Sketch of Proof for Proposition 3.1.2 41
3.2 fc-neaxest neighbor estimates 42
Computational aspects of k-NN smoothing 48
Exercises 49
3.3 Orthogonal series estimators 50
Exercises 55
Complements 55
Sketch of Proof for Proposition 3.3.1 55
3.4 Spline smoothing 56
Exercises 64
vu
viii Contents
Complements 64
Proof of Proposition 3.4.2 64
Proof of equivalence of the Silverman and Huber
approximation 64
3.5 An overview of various smoothers 65
Recursive techniques 66
The regressogram 67
Convolution smoothing 68
Delta function sequence estimators 68
Median smoothing 69
Split linear fits 70
Empirical regression 72
Exercises 73
Complements 74
3.6 A comparison of kernel, k-NN and spline smoothers 75
Exercises 84
Complements 85
PART II. The kernel method 87
Chapter 4. How close is the smooth to the true curve? 89
4.1 The speed at which the smooth curve converges 91
Rates of convergence for nonquadratic distance
measures 95
Exercises 96
Complements 97
4.2 Pointwise confidence intervals 98
Exercises 108
Complements 109
4.3 Variability bands for functions 110
Connected error bars 111
Smooth confidence bands 114
Bootstrap bands 118
Exercises 128
Complements 129
4.4 Behavior at the boundary 130
Exercises 132
4.5 The accuracy as a function of the kernel 133
Exercises 137
Complements 140
4.6 Bias reduction techniques 141
Exercises 146
Contents ix
Chapter 5. Choosing the smoothing parameter 147
5.1 Cross-validation, penalizing functions and the plug-in
method 148
Leave-one-out method, cross-validation 152
Penalizing functions 154
The plug-in method 155
Bandwidth choice for derivative estimation 160
The dependence of the smoothing parameter on the
weight function 162
Exercises 162
Complements 163
5.2 Which selector should be used? 165
Exercises 173
Complements 175
5.3 Local adaptation of the smoothing parameter 177
Improving the smooth locally by bootstrapping 177
The supersmoother 181
Exercises 184
5.4 Comparing bandwidths between laboratories
(canonical kernels) 184
Exercises 189
Chapter 6. Data sets with outliers 190
6.1 Resistant smoothing techniques 191
LOcally WEighted Scatter plot Smoothing (LOWESS) 192
L-smoothing 193
/{-smoothing 194
M-smoothing 195
Exercises 200
Complements 201
Chapter 7. Nonparametric regression techniques for
correlated data 203
7.1 Nonparametric prediction of time series 204
7.2 Smoothing with dependent errors 209
Exercises 215
Complements 215
Chapter 8. Looking for special features and qualitative
smoothing 217
8.1 Monotonic and unimodal smoothing 218
Pool-adjacent-violators (PAV) Algorithm 8.1.1 218
Contents
Exercises 223
Complements 224
8.2 Estimation of zeros and extrema 225
Exercises 230
Complements 230
Chapter 9. Incorporating parametric components 232
9.1 Partial linear models 233
Exercises 236
9.2 Shape-invariant modeling 237
Exercises 243
Complements 243
9.3 Comparing nonparametric and parametric curves 244
Exercises 249
Complements 252
PART III. Smoothing in high dimensions 255
Chapter 10. Investigating multiple regression by additive
models 257
10.1 Regression trees 259
Exercises 264
10.2 Projection pursuit regression 265
Exercises 268
10.3 Alternating conditional expectations 269
Exercises 273
10.4 Average derivative estimation 274
Exercises 280
10.5 Generalized additive models 281
Exercises 286
Appendix 1. A desirable computing environment 291
Appendix 2. Tables 301
References 305
Name index 325
Subject index 329
|
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| indexdate | 2024-07-09T22:00:16Z |
| institution | BVB |
| isbn | 0521382483 |
| language | English |
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| owner_facet | DE-83 |
| physical | XV, 333 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Univ. Pr. |
| record_format | marc |
| series2 | Econometric society monographs |
| spelling | Härdle, Wolfgang 1953- Verfasser (DE-588)110357116 aut Applied nonparametric regression Wolfgang Härdle Repr. Cambridge <<[u.a.]>> Univ. Pr. 1993 XV, 333 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Econometric society monographs Nichtparametrische Regression (DE-588)4745075-7 gnd rswk-swf Nichtparametrische Schätzung (DE-588)4203980-0 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Nichtparametrische Statistik (DE-588)4226777-8 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s Nichtparametrische Statistik (DE-588)4226777-8 s DE-604 Nichtparametrische Schätzung (DE-588)4203980-0 s Nichtparametrische Regression (DE-588)4745075-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018446136&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Härdle, Wolfgang 1953- Applied nonparametric regression Nichtparametrische Regression (DE-588)4745075-7 gnd Nichtparametrische Schätzung (DE-588)4203980-0 gnd Regressionsanalyse (DE-588)4129903-6 gnd Nichtparametrische Statistik (DE-588)4226777-8 gnd |
| subject_GND | (DE-588)4745075-7 (DE-588)4203980-0 (DE-588)4129903-6 (DE-588)4226777-8 |
| title | Applied nonparametric regression |
| title_auth | Applied nonparametric regression |
| title_exact_search | Applied nonparametric regression |
| title_full | Applied nonparametric regression Wolfgang Härdle |
| title_fullStr | Applied nonparametric regression Wolfgang Härdle |
| title_full_unstemmed | Applied nonparametric regression Wolfgang Härdle |
| title_short | Applied nonparametric regression |
| title_sort | applied nonparametric regression |
| topic | Nichtparametrische Regression (DE-588)4745075-7 gnd Nichtparametrische Schätzung (DE-588)4203980-0 gnd Regressionsanalyse (DE-588)4129903-6 gnd Nichtparametrische Statistik (DE-588)4226777-8 gnd |
| topic_facet | Nichtparametrische Regression Nichtparametrische Schätzung Regressionsanalyse Nichtparametrische Statistik |
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