Jon Wellner presents this year’s Le Cam Lecture, given every third year in memory of Lucien Le Cam, at JSM in Seattle.

Jon A. Wellner, born in 1945 in Oregon, graduated in Mathematics and Physics from the University of Idaho in 1968, and received his PhD from the University of Washington in 1975. He began his academic career at the University of Rochester in 1975 as an Assistant Professor of Statistics, and was promoted to Associate Professor in 1981 after a sabbatical leave at the Mathematics Institute at the University of Munich. He returned to the University of Washington as Professor of Statistics in 1983. His research has alternated between statistical issues concerning semiparametric models and asymptotic theory of empirical processes. He gave an IMS Special Invited Lecture (or Medallion Lecture as they are now called) in 1992, and was honored with the Senior Noether Award by the ASA in 2011. In recent years his research has focused on nonparametric statistical inference under shape restrictions.

This IMS Le Cam lecture, Maximum likelihood in modern times: the ugly, the bad, and the good, will be delivered at the JSM on Monday 10 August 2015 in Seattle.

Maximum likelihood in modern times: the ugly, the bad, and the good

Maximum likelihood continues to be a theme in current statistical theory in both parametric and nonparametric settings despite a number of known potential difficulties:

• Maximum likelihood estimators may not exist.

• When MLEs exist, they may not be consistent.

• When MLEs exist and are consistent, they may not attain optimal rates of convergence.

In spite of these difficulties, maximum likelihood has also had a number of success stories in semiparametric and nonparametric problems. The talk will survey some of the difficulties and a selection from recent progress, including:

The ugly: non-existence, non-uniqueness, and inconsistency.

The bad: possible non-attainment of optimal rates in high-dimensional settings.

The good: lack of dependence on tuning parameters, and:

• beyond consistency for Kiefer–Wolfowitz mixture models;

• behavior of profile-likelihood methods for semiparametric models;

• behavior of shape constrained estimators globally, locally, and under model-misspecification.