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

In: Recent Developments in Multivariate and Random Matrix Analysis

Author

Listed:
  • Björn Holmquist

    (Lund University, Department of Statistics)

  • Anna Sjöström

    (Lund University, Department of Statistics)

  • Sultana Nasrin

    (Lund University, Department of Statistics)

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.

Suggested Citation

  • Björn Holmquist & Anna Sjöström & Sultana Nasrin, 2020. "Approximating Noncentral Chi-Squared to the Moments and Distribution of the Likelihood Ratio Statistic for Multinomial Goodness of Fit," Springer Books, in: Thomas Holgersson & Martin Singull (ed.), Recent Developments in Multivariate and Random Matrix Analysis, chapter 0, pages 175-198, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-56773-6_11
    DOI: 10.1007/978-3-030-56773-6_11
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