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Bartlett correction of an independence test in a multivariate Poisson model
Statistica Neerlandica ( IF 1.5 ) Pub Date : 2022-01-30 , DOI: 10.1111/stan.12265
Rolf Larsson 1
Affiliation  

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.

中文翻译:

多元泊松模型中独立性检验的 Bartlett 校正

我们考虑一个因泊松变量系统,其中每个变量是一个独立变量和一个公共变量的总和。产生依赖性的是公共变量。在该系统中,可以构建独立性检验,其中零假设是公共变量相同为零。在本文中,我们考虑最大对数似然比检验。对于这个检验,众所周知,检验统计量的渐近分布是零和一个自由度的卡方分布的等混合。我们检查了检验的 Bartlett 校正,希望我们能更好地逼近中等大样本量的标称大小。明确推导出这种类型的校正,并在模拟研究中探索其有用性。出于实际目的,
更新日期:2022-01-30
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