数学
似然比检验
维数(图论)
统计
无效假设
统计假设检验
替代假设
独立同分布随机变量
空(SQL)
似然原理
指数族
指数函数
随机变量
组合数学
最大似然
似然函数
数学分析
计算机科学
数据库
拟极大似然
作者
Yansong Bai,Yong Zhang
出处
期刊:Random matrices : theory and applications
[World Scientific]
日期:2023-01-09
卷期号:12 (03)
被引量:2
标识
DOI:10.1142/s201032632350003x
摘要
Let [Formula: see text] be independent and identically distributed (i.i.d.) real-valued random vectors from distribution [Formula: see text], where the sample size [Formula: see text] and the vector dimension [Formula: see text] satisfy [Formula: see text]. We are interested in the exponential convergence rate of the likelihood ratio test (LRT) statistics for testing [Formula: see text] equal to a given matrix and [Formula: see text] equal to a given pair. In traditional statistical theory, the LRT statistics have been studied under the null hypothesis and finite-dimensional conditions. In this paper, we prove the moderate deviation principle (MDP) under the high-dimensional conditions for the two LRT statistics. We show that our results hold under the null hypothesis and the alternative hypothesis as well. Some numerical simulations indicate that our conclusions have good performance.
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