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Conditional large deviations for density case

Author

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  • Kim, Gie-Whan
  • Truax, Donald R.

Abstract

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 [greater-or-equal, slanted] 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.

Suggested Citation

  • Kim, Gie-Whan & Truax, Donald R., 1998. "Conditional large deviations for density case," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 137-144, June.
    • Handle: RePEc:eee:stapro:v:38:y:1998:i:2:p:137-144
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