NONPARAMETRIC REGRESSION WITH MEASUREMENT ERROR: SOME RECENT PROGRESS

		David Ruppert

In nonparametric regression we estimate the conditional expectation of
a response Y given a covariate X without assuming a parametric
structure for this function.  In regression with measurement error, we
do not observe X itself but rather a proxy W which is commonly assumed
to be X plus measurement error.  Nonparametric regression without
measurement error has been studied extensively.   Moreover, parametric
regression with measurement error is now a well developed field with
monographs by Fuller (1987) and Carroll, Ruppert, and Stefanski
(1995).  It is perhaps surprising then, that there has been little work
on nonparametric regression with measurement error.  This lack of
research may indicate the difficulty of the problem.  Before the work
of Carroll and Ruppert and their coworkers, Jeff Maca and Scott Berry,
only the paper by Fan and Truong (1993, Annals) was available.

We now have several efficient methodologies for nonparametric
regression with mismeasured X's: SIMEX and local polynomial regression,
SIMEX with penalized splines, a flexible structural spline method, and
a fully Bayesian spline method.  These methodologies will be explained
and compared.

The slides and references for this talk are available at:
www.orie.cornell.edu/~davidr
(link to "recent lectures")