Linton, Oliver and Xiao, Zhijie (2001) A nonparametric regression estimator that adapts to error distribution of unknown form. Econometrics; EM/2001/419, EM/01/419. Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science, London, UK.
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We propose a new estimator for nonparametric regression based on local likelihood estimation using an estimated error score function obtained from the residuals of a preliminary nonparametric regression. We show that our estimator is asymptotically equivalent to the infeasible local maximum likelihood estimator [Staniswalis (1989)], and hence improves on standard kernel estimators when the error distribution is not normal. We investigate the finite sample performance of our procedure on simulated data.
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