Asymptotics of kernel estimators based on local maximum likelihood

Abstract

We consider the kernel estimates of the regression function, which are derived from the local maximum likelihood. Under suitable regularity conditions, strong uniform consistency rates on a compact interval and asymptotic normality are obtained. The rate of convergence obtained here is the same as Stone's (1982) optimal rate for the special case of nonparametric regression in additive models. Also pointwise efficient data driven estimation is possible.

Keywords:

• Kernel estimator
• local maximum likelihood
• strong uniform consistency rate
• asymptotic normality
• adaptive estimate
• AMS 1980 Subject Classifications
• Primary 62J02
• Secondary 62Go5