On approximating some statistics of goodness-of-fit tests in the case of three-dimensional discrete data

Zh A. Asylbekov, V. N. Zubov, V. V. Ulyanov

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We study the rate of weak convergence of the distributions of the statistics {tλ(Y), λ ∈ ℝ} from the power divergence family of statistics to the χ2 distribution. The statistics are constructed from n observations of a random variable with three possible values. We show that, where G2(c) is the χ2 distribution function of a random variable with two degrees of freedom. In the proof we use Huxley's theorem of 1993 on approximating the number of integer points in a plane convex set with smooth boundary by the area of the set.

Original languageEnglish
Pages (from-to)571-584
Number of pages14
JournalSiberian Mathematical Journal
Volume52
Issue number4
DOIs
Publication statusPublished - Jul 1 2011

Keywords

  • Huxley theorem
  • accuracy of χ approximation
  • integer points
  • power divergence family of statistics

ASJC Scopus subject areas

  • Mathematics(all)

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