Abstract :
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+
