JSM 2004 - Toronto

Abstract #301588

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Activity Number: 262
Type: Topic Contributed
Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Graphics
Abstract - #301588
Title: Reduction Algorithm for the MLE for the Distribution Function of Bivariate Interval Censored Data
Author(s): Marloes H. Maathuis*+
Companies: University of Washington
Address: Dept. of Statistics, Seattle, WA, 98195-4322,
Keywords: computational geometry ; parameter reduction ; maximal clique ; maximal intersection ; regions of possible mass support
Abstract:

We study computational aspects of the nonparametric maximum likelihood estimator (MLE) for the distribution function of bivariate interval censored data. The computation of the MLE consists of two steps: a parameter reduction step and an optimization step. We focus on the reduction step. We introduce two new reduction algorithms: the Tree algorithm and the HeightMap algorithm. The Tree algorithm is only mentioned briefly. The HeightMap algorithm is discussed in detail and also given in pseudo-code. It is a very fast and simple algorithm of time complexity O(n^2). This is an order faster than the best known algorithm thus far, the O(n^3) algorithm of Bogaerts and Lesaffre (2003). We compare our algorithms with the algorithms of Gentleman and Vandal (2001), Song (2001) and Bogaerts and Lesaffre (2003) using simulated data. We show that our algorithms, and especially the HeightMap algorithm, are significantly faster.

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