Point Asymptotics for Probabilities of Large Deviations of the ω2 Statistics in Verification of the Symmetry Hypothesis

  • Authors:

  • V. R. Fatalov

  • Affiliations:

  • M.V. Lomonosov Moscow State University

  • Venue:
  • Problems of Information Transmission
  • Year:
  • 2004

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Abstract

We consider the ω2 statistic, destined for testing the symmetry hypothesis, which has the form ωn2 = n ∫−∞∞[Fn(x) + Fn(−x) − 1]2 dFn(x), where Fn(x) is the empirical distribution function. Based on the Laplace method for empirical measures, exact asymptotic (as n → ∞) of the probability Pr{ωn2 nv} for 0 v