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                              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.