Spring 2002 Seminar Series - January 29, 2002
University of Minnesota
School of Statistics
College of Liberal Arts
Error density and distribution function estimation in nonparametric
regression
Fuxia Cheng
Michigan State University
(Statistics Search Candidate)
Tuesday, January 29, 2002
4:00 PM,
B10
Ford Hall
Minneapolis, East Bank Campus
Social at 3:30 PM,
300
Ford Hall
Abstract
Over the last five decades, the statistical literature has been replete with
papers on the estimation of the regression function. Relatively little is known
about the estimation of the error density and distribution functions in these
models. It is often of interest and of practical importance to know the nature
of the error distribution after estimating a regression function.
This talk will discuss some asymptotics of some error density and distribution
function estimators in nonparametric regression models. In particular, the
histogram type density estimators based on nonparametric regression residuals
obtained from the full sample are shown to be uniformly almost surely consistent.
A similar result with a rate is obtained for the empirical d.f. of these
residuals. Furthermore, if one uses a part of the sample to estimate the
regression function and the other part to estimate the error density, then the
asymptotic distribution of the maximum of a suitably normalized deviation of
the density estimator from the true error density function is the same as in
the case of the one sample setup. Similarly, a suitably standardized
nonparametric residual empirical process based on the second part of the
sample is shown to weakly converge to a time transformed Brownian bridge.