[推荐]应用非参数回归

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Contents

I Regression smoothing 1

1 Introduction 3

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2 Scope of this book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2 Basic idea of smoothing 17

2.1 The stochastic nature of the observations . . . . . . . . . . . . . . . . . . . . 26

2.2 Hurdles for the smoothing process . . . . . . . . . . . . . . . . . . . . . . . . 27

3 Smoothing techniques 31

3.1 Kernel Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2 Complements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.3 Proof of Proposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.4 k-nearest neighbor estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.5 Orthogonal series estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.6 Spline smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.7 Complements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.8 An overview of various smoothers . . . . . . . . . . . . . . . . . . . . . . . . 78

3.9 Recursive techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

3.10 The regressogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3.11 A comparison of kernel, k-NN and spline smoothers . . . . . . . . . . . . . . 87

II The kernel method 111

4 How close is the smooth to the true curve? 113

4.1 The speed at which the smooth curve converges . . . . . . . . . . . . . . . . 116

4.2 Pointwise confidence intervals . . . . . . . . . . . . . . . . . . . . . . . . . . 125

4.3 Variability bands for functions . . . . . . . . . . . . . . . . . . . . . . . . . . 139

4.4 Behavior at the boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

4.5 The accuracy as a function of the kernel . . . . . . . . . . . . . . . . . . . . 162

4.6 Bias reduction techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

5 Choosing the smoothing parameter 179

5.1 Cross-validation, penalizing functions and the plug-in method. . . . . . . . . 180

5.2 Which selector should be used? . . . . . . . . . . . . . . . . . . . . . . . . . 200

5.3 Local adaptation of the smoothing parameter . . . . . . . . . . . . . . . . . 214

5.4 Comparing bandwidths between laboratories (canonical kernels) . . . . . . . 223

6 Data sets with outliers 229

6.1 Resistant smoothing techniques . . . . . . . . . . . . . . . . . . . . . . . . . 231

6.2 Complements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

7 Nonparametric regression techniques for time series 245

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

7.2 Nonparametric time series analysis . . . . . . . . . . . . . . . . . . . . . . . 247

7.3 Smoothing with dependent errors . . . . . . . . . . . . . . . . . . . . . . . . 263

7.4 Conditional heteroscedastic autoregressive nonlinear models . . . . . . . . . 267

8 Looking for special features and qualitative smoothing 281

8.1 Monotonic and unimodal smoothing . . . . . . . . . . . . . . . . . . . . . . . 282

8.2 Estimation of Zeros and Extrema . . . . . . . . . . . . . . . . . . . . . . . . 291

9 Incorporating parametric components 299

9.1 Partial linear models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

9.2 Shape-invariant modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

9.3 Comparing nonparametric and parametric curves . . . . . . . . . . . . . . . 313

III Smoothing in high dimensions 325

10 Investigating multiple regression by additive models 327

10.1 Regression trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

10.2 Projection pursuit regression . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

10.3 Alternating conditional expectations . . . . . . . . . . . . . . . . . . . . . . 341

10.4 Average derivative estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 348

10.5 Generalized additive models . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

A XploRe 365

A.1 Using XploRe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365

A.2 Quantlet Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

A.3 Getting Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378

A.4 Basic XploRe Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

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关键词：非参数回归 非参数 introduction observations Expectations 推荐 应用 参数

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【书名】    Applied Nonparametric Regression （实用非参数回归）    

【作者】    Wolfgang Hardle 

【出版社】 Spandauer

【版本】   未知

【出版日期】1994

【文件格式】PDF

【文件大小】4.5M

【页数】 433

【ISBN出版号】无

【资料类别】计量经济学

【市面定价】无

【扫描版还是影印版】清晰版

【是否缺页】无

【关键词】Nonparametric Regression

【内容简介】This book concentrates on the statistical aspects of nonparametric regression smoothing from an applied point of view. The methods covered in this text   be used in biometry, econometrics, engineering and mathematics. The two central problems discussed are the choice of smoothing parameter and the construction of confidence bands in practice. Various smoothing methods among them splines and orthogonal polynomials are presented and discussed in their qualitative aspects. To simplify the exposition kernel smoothers are 18 investigated in greater detail. Most of the results are stated in a rather compact form and proved only in the simplest situations.

【目录】

Contents

I Regression smoothing 1

1 Introduction 3

2 Basic idea of smoothing 17

3 Smoothing techniques 31

4 How close is the smooth to the true curve? 113

5 Choosing the smoothing parameter 179

6 Data sets with outliers 229

7 Nonparametric regression techniques for time series 245

8 Looking for special features and qualitative smoothing 281

9 Incorporating parametric components 299

10 Investigating multiple regression by additive models 327

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