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

doi:10.1134/S0037446611040021

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We study the rate of weak convergence of the distributions of the statistics {t_λ(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 language	English
Pages (from-to)	571-584
Number of pages	14
Journal	Siberian Mathematical Journal
Volume	52
Issue number	4
DOIs	https://doi.org/10.1134/S0037446611040021
Publication status	Published - 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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10.1134/S0037446611040021

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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.",

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AU - Ulyanov, V. V.

PY - 2011/7/1

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N2 - 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.

AB - 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.

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