ruth@utstat.uucp (Ruth Croxford) (05/04/89)
Colloquium
Department of Statistics, University of Toronto
Topic: Nonregular Regression
Speaker:Richard L. Smith
University of Surrey, Guilford, U.K., visiting University of
Chicago
Date: Thursday, May 11, 1989 4:00 p.m.
Place: Room 2128, Sidney Smith Hall, 100 St. George St., University
of Toronto
Abstract:
In an earlier paper (Smith 1985, Biometrika) I considered maximum
likelihood estimation in probability distributions where the unknown
parameters include an unknown endpoint; some examples are the three-
parameter Weibull and gamma distributions. These distributions exhi-
bit a variety of non-standard asymptotic behaviour. The present talk
is aimed at showing how the same ideas may apply in the context of
more general statistical models. Specifically, I consider a regres-
sion model in which there are several covariates acting additively. A
specific estimator is proposed, which depends upon solving a linear
programming problem, and its asymptotic properties are established,
and compared with those of maximum likelihood estimates. Applications
include estimating trends in series of athletics records (Smith 1988,
JASA), studying the influence of covariates on environmental extremes,
and an historical data set on strengths of wooden beams.