Generous statistical tests |
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Authors: | T V Hromadka II R J Whitley S B Horton M J Smith J M Lindquist |
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Institution: | (1) Department of Mathematical Sciences, United States Military Academy, West Point, NY 10096, USA;(2) P.O. Box 11133, Bainbridge Island, WA 98110, USA |
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Abstract: | A common statistical problem is deciding which of two possible sources, A and B, of a contaminant is most likely the actual
source. The situation considered here, based on an actual problem of polychlorinated biphenyl contamination discussed below,
is one in which the data strongly supports the hypothesis that source A is responsible. The problem approach here is twofold:
One, accurately estimating this extreme probability. Two, since the statistics involved will be used in a legal setting, estimating
the extreme probability in such a way as to be as generous as is possible toward the defendant’s claim that the other site
B could be responsible; thereby leaving little room for argument when this assertion is shown to be highly unlikely. The statistical
testing for this problem is modeled by random variables {X
i
} and the corresponding sample mean the problem considered is providing a bound ɛ for which for a given number a
0. Under the hypothesis that the random variables {X
i
} satisfy E(X
i
) ≤ μ, for some 0 < μ < 1, statistical tests are given, described as “generous”, because ɛ is maximized. The intent is to
be able to reject the hypothesis that a
0 is a value of the sample mean while eliminating any possible objections to the model distributions chosen for the {X
i
} by choosing those distributions which maximize the value of ɛ for the test used. |
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Keywords: | Testing unlikely events Extreme deviations PCB contamination |
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