Handbook of Econometrics Vols1-5 _ Chapter 38

Chapter 38 APPLIED WOLFGANG NONPARAMETRIC Although economic theory generally provides only loose restrictions on the distribution of observable quantities, much econometric work is based on tightly specified parametric models and likelihood based methods of inference. | Chapter 38 APPLIED NONPARAMETRIC METHODS WOLFGANG HÄRDLE Humboldt-Universität Berlin OLIVER LINTON1 Oxford University Contents Abstract 2297 1. Nonparametric estimation in econometrics 2297 2. Density estimation 2300 . Kernels as windows 2300 . Kernels and ill-posed problems 2301 . Properties of kernels 2302 . Properties of the kernel density estimator 2303 . Estimation of multivariate densities their derivatives and bias reduction 2304 . Fast implementation of density estimation 2306 3. Regression estimation 2308 . Kernel estimators 2308 . k-Nearest neighbor estimators 2310 . Ordinary k-NN estimators 2310 . Symmetrized k-NN estimators 2311 . Local polynomial estimators 2311 . Spline estimators 2312 . Series estimators 2313 . 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 Pôle d attraction interuniversitaire of the Belgian government. fWe 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 Miiller this work would not have been possible. Handbook of Econometrics Volume IV Edited by . Engle and . McFadden 1994 Elsevier Science . All rights reserved 2296 W. Hardie and O. Linton . Confidence intervals 2315 . Regression derivatives and quantiles 2318 4. Optimality and bandwidth choice 2319 . Optimality 2319 . Choice of smoothing parameter 2321 . Plug-in 2322 . Crossvalidation 2322 . Other data driven selectors 2323 5. Application to time series 2325 . Autoregression 2326 . Correlated errors 2327 6. Applications to semiparametric estimation 2328 . The partially linear model 2329 . Heteroskedastic nonlinear regression 2330 . Single index models 2331 7. Conclusions 2334 .