In this paper we investigate the asymptotic distribution of likelihood ratio tests in models with several groups, when the number of groups converges with the dimension and sample size to infinity. We derive central limit theorems for the logarithm of various test statistics and compare our results with the approximations obtained from a central limit theorem using a two step procedure: first consider the number of groups fixed and assume that the sample size and dimension converge to infinity, secondly investigating the resulting distribution if the number of groups converges to infinity.

中文翻译：

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高维多组的似然比检验

在本文中，我们研究了当组数与维度和样本大小收敛到无穷大时，多组模型中似然比检验的渐近分布。我们推导出各种检验统计量的对数的中心极限定理，并将我们的结果与使用两步程序从中心极限定理获得的近似值进行比较：首先考虑固定的组数，并假设样本大小和维度收敛到无穷大，其次，如果组数收敛到无穷大，则调查结果分布。