Abstract #300621


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JSM 2002 Abstract #300621
Activity Number: 11
Type: Topic Contributed
Date/Time: Sunday, August 11, 2002 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #300621
Title: Likelihood Ratio Inference for Case 1 Interval Censoring and Related Models
Author(s): Moulinath Banerjee*+
Affiliation(s): University of Michigan
Address: 4081, Frieze Building 105 S.State St., Ann Arbor, Michigan, 48109-1285, USA
Keywords: Brownian motion ; greatest convex minorant ; interval censoring ; likelihood ratio statistic
Abstract:

I will discuss the problem of testing for equality at a fixed point in the context of nonparametric estimation of a monotone function and specifically in the context of the Case 1 interval censoring model, where the monotone function of interest is the distribution function of the survival time. The class of models of interest differs markedly from regular models in that maximum likelihood estimators of the monotone function of interest converge at a slower (n^{1/3}) rate to a non-Gaussian limiting variable, which is characterized by the slope of standard two-sided Brownian motion + t^2 at 0. The behavior of the likelihood ratio statistic is investigated in the particular case of interval censoring (Case 1 or current status data) and the limit distribution under the null hypothesis is obtained. The limit no longer belongs to the usual chi-squared family but is characterized as the integral of the difference of the squared slope processes corresponding to a canonical version of the problem involving Brownian motion + t^2 and greatest convex minorants thereof. Furthermore, the limit distribution is universal - it does not depend on the underlying parameters in the problem.


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