JSM 2004 - Toronto

Abstract #301803

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Activity Number: 22
Type: Contributed
Date/Time: Sunday, August 8, 2004 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #301803
Title: Nonparametric Simultaneous Confidence Bands for Current Status Data
Author(s): Michael R. Kosorok*+
Companies: University of Wisconsin, Madison
Address: K6/428 Clinical Science Center, Madison, WI, 53792-4675,
Keywords: current status data ; extreme value distribution ; confidence bands ; nonparametric maximum likelihood ; bootstrap ; rate of convergence
Abstract:

We study the problem of constructing simultaneous confidence bands for the cumulative distrubution function based on nonparametric maximum likelihood estimation (NPMLE) with current status data. Recent results by Hooghiemstra and Lopuhaa (1998) and Groeneboom (1989) shed light on the extremal limit behavior of the uniform norm of the NPMLE minus the true distribution. We verify that this norm, after suitable standardization, converges to the extreme value distribution. We study the uniform rate of convergence to this extreme value distribution, and show that the rate can be significantly improved through use of the bootstrap.

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