Probabilities of Large Deviations of Type II Errors for Tests of Kolmogorov and Omega-Square Types

Abstract

For the Kolmogorov and omega-square tests, strong asymptotics for large deviations of type II error probabilities are obtained in the case of “least favorable alternatives.” Using these asymptotics, type II error probabilities for any sequence of alternatives can readily be estimated. The proofs are based on an exact asymptotic of large deviation probabilities for Gaussian measures in a Hilbert space and on a theorem on large deviation probabilities for sums of independent random vectors in a Banach space. Bibliography: 22 titles.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 298, 2003, pp. 80–110.

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Ermakov, M.S. Probabilities of Large Deviations of Type II Errors for Tests of Kolmogorov and Omega-Square Types. J Math Sci 128, 2538–2555 (2005). https://doi.org/10.1007/s10958-005-0201-4

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Keywords

  • Hilbert Space
  • Banach Space
  • Random Vector
  • Error Probability
  • Gaussian Measure