Applied Nonparametric Regression

Wolfgang Härdle9780521429504, 0521429501

The applications and problems of two central aspects – the choice of smoothing parameters and the construction of confidence bounds – are focused on in an original presentation of the techniques for regression curve smoothing involving more than one variable.

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Table of contents :
Regression smoothing……Page 25
Introduction……Page 27
Motivation……Page 31
Scope of this book……Page 38
Basic idea of smoothing……Page 41
The stochastic nature of the observations……Page 50
Hurdles for the smoothing process……Page 51
Smoothing techniques……Page 55
Kernel Smoothing……Page 56
Proof of Proposition……Page 73
k-nearest neighbor estimates……Page 76
Orthogonal series estimators……Page 85
Spline smoothing……Page 94
Complements……Page 101
Recursive techniques……Page 102
The regressogram……Page 104
A comparison of kernel, k-NN and spline smoothers……Page 111
The kernel method……Page 135
How close is the smooth to the true curve?……Page 137
The speed at which the smooth curve converges……Page 140
Pointwise confidence intervals……Page 149
Variability bands for functions……Page 163
Behavior at the boundary……Page 183
The accuracy as a function of the kernel……Page 186
Bias reduction techniques……Page 196
Choosing the smoothing parameter……Page 203
Cross-validation, penalizing functions and the plug-in method…….Page 204
Which selector should be used?……Page 224
Local adaptation of the smoothing parameter……Page 238
Comparing bandwidths between laboratories (canonical kernels)……Page 247
Data sets with outliers……Page 253
Resistant smoothing techniques……Page 255
Complements……Page 265
Introduction……Page 269
Nonparametric time series analysis……Page 271
Smoothing with dependent errors……Page 287
Conditional heteroscedastic autoregressive nonlinear models……Page 291
Looking for special features and qualitative smoothing……Page 305
Monotonic and unimodal smoothing……Page 306
Estimation of Zeros and Extrema……Page 315
Incorporating parametric components……Page 323
Partial linear models……Page 326
Shape-invariant modeling……Page 330
Comparing nonparametric and parametric curves……Page 337
Smoothing in high dimensions……Page 349
Investigating multiple regression by additive models……Page 351
Regression trees……Page 353
Projection pursuit regression……Page 361
Alternating conditional expectations……Page 365
Average derivative estimation……Page 372
Generalized additive models……Page 378
Using XploRe……Page 389
Quantlet Examples……Page 397
Getting Help……Page 402
Basic XploRe Syntax……Page 405
Tables……Page 411
Bibliography……Page 414
Index……Page 415