多元线性模型特征根的高维渐近分布及典型相关分析

IF 0.5 4区数学 Q3 MATHEMATICS

Hiroshima Mathematical Journal Pub Date : 2017-11-01 DOI:10.32917/HMJ/1509674447

Y. Fujikoshi

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引用次数: 9

摘要

本文导出了多元线性模型在维数p和样本量n较大时特征根的渐近分布。给出了种群特征根的多重度大于1，阶数为O(np)或O(n)的结果。接下来，假设总体典型相关的阶数为O(√p)或O(1)，当其中一个维度和样本量较大时，给出了典型相关的渐近分布的类似结果。AMS 2000学科分类:初级62H10;二次62 e20

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High-dimensional asymptotic distributions of characteristic roots in multivariate linear models and canonical correlation analysis

In this paper, we derive the asymptotic distributions of the characteristic roots in multivariate linear models when the dimension p and the sample size n are large. The results are given for the case that the population characteristic roots have multiplicities greater than unity, and their orders are O(np) or O(n). Next, similar results are given for the asymptotic distributions of the canonical correlations when one of the dimensions and the sample size are large, assuming that the order of the population canonical correlations is O( √ p) or O(1). AMS 2000 Subject Classification: primary 62H10; secondary 62E20

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来源期刊

Hiroshima Mathematical Journal 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Hiroshima Mathematical Journal (HMJ) is a continuation of Journal of Science of the Hiroshima University, Series A, Vol. 1 - 24 (1930 - 1960), and Journal of Science of the Hiroshima University, Series A - I , Vol. 25 - 34 (1961 - 1970). Starting with Volume 4 (1974), each volume of HMJ consists of three numbers annually. This journal publishes original papers in pure and applied mathematics. HMJ is an (electronically) open access journal from Volume 36, Number 1.