Semiparametric Optimality Under Nonstandard Conditions

• Activity Number: 489
• Type: Invited
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Michael R. Kosorok*+
• Companies: The University of North Carolina at Chapel Hill
• Keywords: semiparametric optimality ; non-identifiability ; constrained estimation

Abstract

We consider semiparametric optimality under two non-standard conditions. The first condition happens when the semiparametric model has a parameter that is not identifiable under a null hypothesis being tested. The second condition happens when there are a finite number of smooth inequality constraints on the parameters. In both settings, careful attention must be paid to local asymptotic normality. This is particularly true in the first setting where the appropriate limiting distribution is a Gaussian process rather than the usual Gaussian vector. In the second setting, minimaxity and admissibility for the constrained estimator boil down to minimaxity and admissibility for a single, multivariate normal observation with mean constrained to a cone and variance unknown. Unfortunately, finding either minimax or admissible estimators for this single normal observation case is currently an unsolved problem. Recent developments on these problems will be discussed along with several open questions.