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ISSN : 1226-0657

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Vol.4 No.1
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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1997, v.4 no.1, pp.97-104
Kim, Gie-Whan
Kim,, G. (1997). . Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 4(1), 97-104.
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Abstract

The large deviations theorem of Cramer is extended to conditional probabilities in the following sense. Consider a random sample of pairs of random vectors and the sample means of each of the pairs. The probability that the first falls outside a certain convex set given that the second is fixed is shown to decrease with the sample size at an exponential rate which depends on the Kullback-Leibler distance between two distributions in an associated exponential familiy of distributions. Examples are given which include a method of computing the Bahadur exact slope for tests of certain composite hypotheses in exponential families.

keywords
large deviations, exponential families, testing hypotheses, Kullback-Leibler information

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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