Extreme Quantile Estimation in Binary Response Models
ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD
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Binary response models are used in estimating the probability, Px, of a successful response when an experimental unit is exposed to a stimulus level, x. Frequently, the aim of the investigator is to locate a specific level of stimulus for which Px takes on a known value, p. The stimulus level sought, X sub 100 p, is referred to as the P sub th quantile of Px. When p lies outside the interval .25,.75, X sub 100 p is considered to be an extreme quantile. The focus of this paper is the estimation of extreme X sub 100 p. All estimation techniques for extreme quantiles seek to limit estimate bias, lack of precision, and the importance of parametric assumption. The extreme quantile estimate described here utilizes, through a transformation of the responses, median estimation techniques where such problems are not so acute. The feasibility of the approach is demonstrated in a Monte Carlo study. It is shown that the design aspect of the approach has properties important to c-optimality, and it is argued that most data sets should be fit well by the modeled employed. This paper also explores the relationship between data structure and the existence of maximum likelihood estimates in finite samples.
- Statistics and Probability