Title:    After Maximum Likelihood, What?


Abstract:


Maximum likelihood estimation is universal but
sensitive to model misspecification and outliers.
Careful examination of the likelihood estimation
equations reveals how they may be modified to reduce
the influence of bad data.  The resulting M-estimators
are particularly important with massive data sets
for which manual data checking is not feasible.

In this talk we examine an alternative approach
based upon a minimum distance criterion.  The goal
is to find a parametric estimate so that the
estimated density curve is close to the true density
function according to some norm (such as $L_2$).
The formulation of the new criterion and its extension
to regression and mixture estimation problems
is discussed.  This approach is inherently robust
against outliers.  But of more interest, this approach
is self-scaling.  Yet the theoretical behavior is similar
to that of the M-estimators.

The robustness of the procedure is demonstrated by example.
The criterion may be extended to fitting a number of models.
Two case studies are given.  Mixture models are fitted by
the new algorithm and by the EM algorithm to a series of
yearly income samples from Great Britain.  A more complex
application involves estimating a stochastic frontier function
of U.S. Bank performance where the data are assumed to be noisy.
This talk presumes knowledge of only the basics of
data fitting and linear regression.