APPLIED NONPARAMETRIC METHODS

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 * This work was prepared while the first author was visiting CentER, KUB Tilburg, The Netherlands. It was financed, in part, by contract No 26 of the programme "P61e d'attraction interuniversitaire" of the Belgian government. *We would like to thank Don Andrews, Roger Koenker, Jens Perch Nielsen, Tom Rothenberg and Richard Spady for helpful comments. Without the careful typewriting of Mariette Huysentruit and the skillful programming of Marlene Mfiller this work would not have been possible. Handbook of Econometrics, Volume IV, Edited by R.F. Engle and D.L. McFadden © 1994 Elsevier Science B.V. All rights reserved 2296 W. Hiirdle and O. Linton 3.7. Confidence intervals 3.8. Regression derivatives and quantiles 4. O p t i m a l i t y a n d b a n d w i d t h cho ice 4.1. Optimality 4.2. Choice of smoothing parameter 4.2.1. Plug-in 4.2.2. Crossvalidation 4.2.3. Other data driven selectors 5. A p p l i c a t i o n to t ime series 5.1. Autoregression 5.2. Correlated errors 6. A p p l i c a t i o n s to s e m i p a r a m e t r i c e s t i m a t i o n 6.1. The partially linear model 6.2. Heteroskedastic nonlinear regression 6.3. Single index models 7. C o n c l u s i o n s References 2315 2318 2319 2319 2321 2322 2322 2323 2325 2326 2327 2328 2329 233