Moulinath Banerjee, Department of Statistics, University of Washington
"Likelihood Ratio Inference in a Class of Non-regular Problems."
Friday, May 26, 2000
Thompson 325 at 2:30 P.M.
Abstract
We discuss likelihood ratio inference in a class of non-regular problems. These are non-parametric problems where the maximum likelihood estimators of the parameter of interest converge at n1/3 rate to a non-Gaussian limit distribution. In each of these problems the null-hypothesis corresponds to constraining a monotone function at some pre-fixed point of interest. We study the interval censoring model in detail and establish a universal asymptotic distribution for the likelihood ratio statistic. This is obtained as the distribution of a functional of standard two-sided Brownian motion with parabolic drift. We conjecture that the same asymptotic distribution characterizes the limiting behavior of the likelihood ratio statistic in other problems.
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