Title:  Partial Mixture Estimation For Handling Outliers in Data and Regression

Abstract:

        In this talk, I describe an alternative approach to
        formulating some robust M-estimates.  Robust estimation
        provides a powerful solution to practical problems in
        applied statistics.  Simple tasks such as data cleaning
        may be prohibitively expensive with large datasets.
	Our techniques also aim to handle the difficult
	situation where a dataset contains large clusters
	of outliers.  For example, a multi-component normal
	mixture model may be estimated with the expectation
	that several components will identify groups of
	outliers.  We examine this latter idea when we
	deliberately fit a mixture model with fewer
	components than required to pick up all outliers.

        In our formulation, maximum likelihood is replaced
        by a data-based minimum-distance criterion.
        The usual M-estimator specification of the shape and
        scale of the influence function is replaced
        by a single choice of a distribution function for
        the data.  This idea is illustrated for several
        common choices of data, including Gaussian.

	Similar ideas have application in regression.  I am
	interested not only in the case of outlier-contaminated
	regression but also in the case of mixtures of regressions,
	with outliers.  Examples of our approach will be given.