LOCAL MAXIMUM-LIKELIHOOD-ESTIMATION AND INFERENCE

Local maximum likelihood estimation is a nonparametric counterpart of the widely used parametric maximum likelihood technique. It extends th e scope of the parametric maximum likelihood method to a much wider cl ass of parametric spaces. Associated with this nonparametric estimatio n scheme is the issue of bandwidth selection and bias and variance ass essment. This paper provides a unified approach to selecting a bandwid th and constructing confidence intervals in local maximum likelihood e stimation. The approach is then applied to least squares nonparametric regression and to nonparametric logistic regression. Our experiences in these two settings show that the general idea outlined here is powe rful and encouraging.