A NONPARAMETRIC REGRESSION ESTIMATOR THAT ADAPTS TO ERROR DISTRIBUTION OF UNKNOWN FORM

We propose a new kernel estimator for nonparametric regression with unknown error distribution+ We show that the proposed estimator is adaptive in the sense that it is asymptotically equivalent to the infeasible local likelihood estimator ~Staniswalis, 1989, Journal of the American Statistical Association 84, 276–283; Fan, Farmen, and Gijbels, 1998, Journal of the Royal Statistical Society, Series B 60, 591– 608; and Fan and Chen, 1999, Journal of the Royal Statistical Society, Series B 61, 927–943!, which requires knowledge of the error distribution+ Hence, our estimator improves on standard nonparametric kernel estimators when the error distribution is not normal+ A Monte Carlo experiment is conducted to investigate the finite-sample performance of our procedure+