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

Björn Holmquist (), Anna Sjöström () and Sultana Nasrin ()
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Björn Holmquist: Lund University, Department of Statistics
Anna Sjöström: Lund University, Department of Statistics
Sultana Nasrin: Lund University, Department of Statistics

Chapter Chapter 11 in Recent Developments in Multivariate and Random Matrix Analysis, 2020, pp 175-198 from Springer

Abstract: 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 G 2, the likelihood ratio statistic for testing goodness of fit in a s category multinomial distribution. The first two moments of G 2 are used to fit the distribution of G 2 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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-56773-6_11

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DOI: 10.1007/978-3-030-56773-6_11

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