Asymptotic distributions for goodness-of-fit statistics in a sequence of multinomial models

L. Györfi, I. Vajda

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We consider f-disparities Df(p̂n, pn) between discrete distributions pn = (pn1,..., pnkn) and their estimates p̂n = (p̂n1,..., p̂nkn) based on relative frequencies in an i.i.d. sample of size n, where f : (0, ∞) → ℝ is twice continuously differentiable in a neighborhood of 1 with f″(1) ≠ 0. We derive asymptotic distributions of the disparity statistics n Df(p̂n, pn) under certain assumptions about pn and the second derivatives f″ in a neighborhood of 1. These assumptions are weaker than those known from the literature.

Original languageEnglish
Pages (from-to)57-67
Number of pages11
JournalStatistics and Probability Letters
Volume56
Issue number1
DOIs
Publication statusPublished - Jan 1 2002

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Multinomial Model
Goodness of fit
Asymptotic distribution
Statistics
Discrete Distributions
Continuously differentiable
Second derivative
Estimate
Derivatives
Discrete distributions

Keywords

  • Asymptotic distributions
  • Disparity statistics
  • Goodness-of-fit statistics
  • Goodness-of-fit tests

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

Asymptotic distributions for goodness-of-fit statistics in a sequence of multinomial models. / Györfi, L.; Vajda, I.

In: Statistics and Probability Letters, Vol. 56, No. 1, 01.01.2002, p. 57-67.

Research output: Contribution to journalArticle

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