(1) Département de Mathématiques et de Statistique, Université Laval, G1K 7P4, Québec, Canada
Abstract:
Maximum likelihood estimation is considered in the context of infinite dimensional parameter spaces. It is shown that in some
locally convex parameter spaces sequential compactness of the bounded sets ensures the existence of minimizers of objective
functions and the consistency of maximum likelihood estimators in an appropriate topology. The theory is applied to revisit
some classical problems of nonparametric maximum likelihood estimation, to study location parameters in Banach spaces, and
finally to obtain Varadarajan’s theorem on the convergence of empirical measures in the form of a consistency result for a
sequence of maximum likelihood estimators. Several parameter spaces sharing the crucial compactness property are identified.
This research was supported by grants from the National Sciences and Engineering Research Council of Canada and the Fonds
FCAR de la Province de Québec.