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Conditional large deviations for density case

✍ Scribed by Gie-Whan Kim; Donald R. Truax

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
335 KB
Volume
38
Category
Article
ISSN
0167-7152

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✦ Synopsis

The conditional large deviations theorem of Jing and Robinson (1994) is extended in the following sense. Consider a random sample of pairs of random vectors and the sample means of each of the pairs. For p >~ 1, the probability that first falls outside a certain p-dimensional 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.

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In this paper, we prove an exponential rate of convergence result for a common estimator of conditional value-at-risk for bounded random variables. The bound on optimistic deviations is tighter while the bound on pessimistic deviations is more general and applies to a broader class of convex risk me