Asymptotic distribution of the largest off-diagonal entry of correlation matrices期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Asymptotic distribution of the largest off-diagonal entry of correlation matrices

Authors:	Wang Zhou

Institution:	Department of Statistics and Applied Probability, National University of Singapore, Singapore, 117546

Abstract:	Suppose that we have observations from a -dimensional population. We are interested in testing that the variates of the population are independent under the situation where goes to infinity as $n\to \infty$ . A test statistic is chosen to be $L_n=\max_{1\le i< j\le p}\vert\rho_{ij}\vert$ , where $\rho_{ij}$ is the sample correlation coefficient between the -th coordinate and the -th coordinate of the population. Under an independent hypothesis, we prove that the asymptotic distribution of is an extreme distribution of type , by using the Chen-Stein Poisson approximation method and the moderate deviations for sample correlation coefficients. As a statistically more relevant result, a limit distribution for $l_n=\max_{1\le i< j\le p}\vert r_{ij}\vert$ , where $r_{ij}$ is Spearman's rank correlation coefficient between the -th coordinate and the -th coordinate of the population, is derived.

Keywords:	Sample correlation matrices Spearman's rank correlation matrices Chen-Stein method moderate deviations

	点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文