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Approximating Noncentral Chi-Squared to the Moments and Distribution of the Likelihood Ratio Statistic for Multinomial Goodness of Fit

Holmquist, Björn LU orcid ; Sjöström, Anna LU and Nasrin, Sultana LU (2020)
Abstract
The chi-square distribution is often assumed to hold for the asymptotic distribution of two times the log likelihood ratio statistic under the null hypothesis. Approximations are derived for the mean and variance of G2, the likelihood ratio statistic for testing goodness of fit in a s category multinomial distribution. The first two moments of G2 are used to fit the distribution of G2 to a noncentral chi-square distribution. The fit is generally better than earlier attempts to fit to scaled versions of asymptotic central chi-square distributions. The results enlighten the complex role of the dimension of the multivariate variable in relation to the sample size, for asymptotic likelihood ratio distribution results to hold.
Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Recent Developments in Multivariate and Random Matrix Analysis : Festschrift in Honour of Dietrich von Rosen - Festschrift in Honour of Dietrich von Rosen
editor
Holgersson, Thomas and Singull, Martin
publisher
Springer Nature
external identifiers
  • scopus:85149340321
ISBN
978-3-030-56773-6
978-3-030-56772-9
DOI
10.1007/978-3-030-56773-6_11
language
English
LU publication?
yes
id
d07a7d9a-99ae-498d-9c53-f0e916d4fac0
date added to LUP
2022-02-02 14:04:17
date last changed
2025-04-04 14:48:57
@inbook{d07a7d9a-99ae-498d-9c53-f0e916d4fac0,
  abstract     = {{The chi-square distribution is often assumed to hold for the asymptotic distribution of two times the log likelihood ratio statistic under the null hypothesis. Approximations are derived for the mean and variance of G2, the likelihood ratio statistic for testing goodness of fit in a s category multinomial distribution. The first two moments of G2 are used to fit the distribution of G2 to a noncentral chi-square distribution. The fit is generally better than earlier attempts to fit to scaled versions of asymptotic central chi-square distributions. The results enlighten the complex role of the dimension of the multivariate variable in relation to the sample size, for asymptotic likelihood ratio distribution results to hold.}},
  author       = {{Holmquist, Björn and Sjöström, Anna and Nasrin, Sultana}},
  booktitle    = {{Recent Developments in Multivariate and Random Matrix Analysis : Festschrift in Honour of Dietrich von Rosen}},
  editor       = {{Holgersson, Thomas and Singull, Martin}},
  isbn         = {{978-3-030-56773-6}},
  language     = {{eng}},
  publisher    = {{Springer Nature}},
  title        = {{Approximating Noncentral Chi-Squared to the Moments and Distribution of the Likelihood Ratio Statistic for Multinomial Goodness of Fit}},
  url          = {{http://dx.doi.org/10.1007/978-3-030-56773-6_11}},
  doi          = {{10.1007/978-3-030-56773-6_11}},
  year         = {{2020}},
}