Estimating the distribution function of a transformed random vector |
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Authors: | Thomas C. Baker Jr Robert L Sielken Jr |
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Affiliation: | 1. University of South Carolina , Columbia, S. C, 29208;2. Texas A &3. M University , College Station, TX, 77843 |
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Abstract: | Frequently a random vector Y with known distribution function is readily observed. However, the random variable of interest is a transformation of Y say h(Y), and sample values of h are expensive to evaluate. The objective is to estimate the distribution function of using only a small sample on Y. Four estimators are proposed for use when Y is discrete. A Monte Carlo study of the estimators is presented This estimation problem frequently arises when Y is a parameter in a mathematical programming problem and h(Y) is the optimal objective function value. Two examples of this type are presented. |
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Keywords: | nonparametric estimation empirical distribution function percentiles transformed random variables mathematical programming |
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