Goodness of Fit Testing for Errors in Non-Parametric Regression

The usual empirical process based on residuals (or estimated errors) has a
limiting distribution which depends on both the hypothesis and the
non-parametric estimator of the regression function. This dependence may seem
natural and unavoidable. However, it means that distribution of goodness of
fit statistics based on this process, has to be evaluated anew for each
regression function, each estimator of this regression function, and each
hypothesis. Since non-parametric estimation of regression function is
computationally demanding procedure, we can not rely in this task on
computational tools like bootstrap.

However, it will be shown that, at a very little cost, one can have a version
of the empirical process, which are not only distribution free, but will also
actually converge to a standard Brownian motion.

Somewhat surprising fact is that no matter what is the hypothesis and what
estimator is used, this process leads, in general, to tests with better
power.


You are invited to wine and cheese in the staffroom, following the seminar.

A table containing the speakers and dates for UNSW statistics seminars,
Semester 1 2007 is available at
http://www.maths.unsw.edu.au/statistics/statsevents.html

Time: 4pm Friday 13th July, 2007