Abstract #300232

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JSM 2003 Abstract #300232
Activity Number: 98
Type: Contributed
Date/Time: Monday, August 4, 2003 : 9:00 AM to 10:50 AM
Sponsor: Section on Physical and Engineering Sciences
Abstract - #300232
Title: Model Reduction in Estimation of Extreme Quantiles in Multiple Parameter Models for Survival Distributions
Author(s): Elliott Nebenzahl*+ and Dean H. Fearn
Companies: California State University and California State University
Address: Department of Statistics, Hayward, CA, 94542,
Keywords: reliability ; survival ; quantiles ; parametric methods ; model reduction ; estimation
Abstract:

A model reduction technique based on the ratio of estimates of extreme quantiles is introduced. We consider, for example, the 3-parameter exponentiated Weibull family with two shape parameters and one scale parameter. Special cases in this 3-parameter family are the 2-parameter Weibull family and the 2-parameter generalized exponential family. A special case of each of these 2-parameter families is the 1-parameter exponential family. In this setting consider the problem of estimating extreme quantiles such as the .01 or the .99 quantiles. We discuss indifference zones 1 and 2, represented by a collection of parameter settings in the 3-parameter family. In zone I (i=1,2), the researcher is comfortable working within the i-parameter family. This is defined to be so for parameter settings in the 3-parameter family when the ratio of a quantile for the 3-parameter family relative to the same quantile in the i-parameter family is "close" to 1. We develop these indifference zones asymptotically and also by Monte Carlo for fixed sample sizes. A comparison is made between the current approach and more traditional approaches for model reduction, such as by likelihood ratio methods.

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