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Central Limit Theorems for Classical Likelihood Ratio Tests for High-Dimensional Normal Distributions
澳门新葡8455最新网站:2013年06月25日 00:00 点击数:

报告人:Tiefeng Jiang

报告地点:澳门新葡8455最新网站501室

报告澳门新葡8455最新网站:2013年06月26日16:00-17:00

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报告摘要:

For random samples of size n obtained from p-variate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the high-dimensional setting. These test statistics have been extensively studied in multivariate analysis and their limiting distributions under the null hypothesis were proved to be chi-square distributions as n goes to infinity and p remains fixed. In this talk, we consider the high-dimensional case where both p and n go to infinity with p/n → y ∈ (0, 1]. We prove that the likelihood ratio test statistics under this assumption will converge in distribution to normal distributions with explicit means and variances. We perform the simulation study to show that the likelihood ratio tests using our central limit theorems outperform those using the traditional chi-square approximations for analyzing high-dimensional data.

主讲人概况:

美国明尼苏达大学统计新葡京最新官网教授, 吉林大学唐敖庆讲座教授. 主要研究领域是:随机矩阵和高维统计学。

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