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Bartlett correction of an independence test in a multivariate Poisson model

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  • Rolf Larsson

Abstract

We consider a system of dependent Poisson variables, where each variable is the sum of an independent variate and a common variate. It is the common variate that creates the dependence. Within this system, a test of independence may be constructed where the null hypothesis is that the common variate is identically zero. In the present paper, we consider the maximum log likelihood ratio test. For this test, it is well‐known that the asymptotic distribution of the test statistic is an equal mixture of zero and a chi‐square distribution with one degree of freedom. We examine a Bartlett correction of the test, in the hope that we will get better approximation of the nominal size for moderately large sample sizes. A correction of this type is explicitly derived, and its usefulness is explored in a simulation study. For practical purposes, the correction is found to be useful in dimension two, but not in higher dimensions.

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  • Rolf Larsson, 2022. "Bartlett correction of an independence test in a multivariate Poisson model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(4), pages 391-417, November.
    • Handle: RePEc:bla:stanee:v:76:y:2022:i:4:p:391-417
    DOI: 10.1111/stan.12265
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    References listed on IDEAS

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    1. Takesi Hayakawa, 1977. "The likelihood ratio criterion and the asymptotic expansion of its distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 29(1), pages 359-378, December.
    2. Rolf Larsson, 2020. "Discrete factor analysis using a dependent Poisson model," Computational Statistics, Springer, vol. 35(3), pages 1133-1152, September.
    3. Dimitris Karlis, 2003. "An EM algorithm for multivariate Poisson distribution and related models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(1), pages 63-77.
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