한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)
- 제4권1호
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- Pages.97-104
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- 1997
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- 1226-0657(pISSN)
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- 2287-6081(eISSN)
CONDITIONAL LARGE DEVIATIONS FOR 1-LATTICE DISTRIBUTIONS
초록
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.