高斯随机变量经验相关系数的中偏差原理

Moderate deviation for the empirical correlation coefficient of two Gaussian random variables

主要研究两个高斯随机变量X和Y经验相关系数的中偏差原理。我们主要分EX、EY均已知和均未知两种情况分别进行讨论,利用多元统计分析中的结论得出文中考虑的变量Sn*和■n*即为相关系数的极大似然估计,再利用文献[3]的结果、方法和多元统计分析其中的原理,分别证明了X和Y的经验相关系数的中偏差原理,并给出了精确的速率函数。

In this paper, the mederate deviation principle for the empirical correlation coefficient of two Gaussian random variables EX and EY is considered. Under two different cases, i. e. EX, EY both known and EX, EY both unknown, the following Sn^＊ and S^＊ are the maximum likelihood estimations for their correlation coefficient respectively. Then by Gao[ 3 ], we establish the medemte deviation principle for the empirical correlation coefficient of two Gaussian random variables EX and EY, is established and the precise rate function is given.