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Chapter 38
APPLIED NONPARAMETRIC METHODS
WOLFGANG H;iRDLE*
Humboldt-Universitiit Berlin
OLIVER LINTON’
Oxford University
Contents
Abstract 2297
1. Nonparametric estimation in econometrics 2297
2. Density estimation 2300
2.1. Kernels as windows 2300
2.2. Kernels and ill-posed problems 2301
2.3. Properties of kernels 2302
2.4, Properties of the kernel density estimator 2303
2.5. Estimation of multivariate densities, their derivatives and bias reduction 2304
2.6. Fast implementation of density estimation 2306
3. Regression estimation 2308
3.1. Kernel estimators 2308
3.2. k-Nearest neighbor estimators 2310
3.2.1. Ordinary k-NN estimators 2310
3.2.2. Symmetrized k-NN estimators 2311
3.3. Local polynomial estimators 2311
3.4. Spline estimators 2312
3.5. Series estimators 2313
3.6. Kernels, k-NN, splines, and series 2314
3.7. Confidence intervals 2315
3.8. Regression derivatives and quantiles 2318
4. Optimality and bandwidth choice 2319
4.1. Optimality 2319
4.2. Choice of smoothing parameter 2321
4.2.1. Plug-in 2322
4.2.2. Crossvalidation 2322
4.2.3. Other data driven selectors 2323
5. Application to time series 2325
5. I Autoregression 2326
5.2. Correlated errors 2321
6. Applications to semiparametric estimation 2328
6. I The partially linear model 2329
6.2. Heteroskedastic nonlinear regression 2330
6.3. Single index models 233 I
7. Conclusions 2334
References 2334
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