A Discussion for Test of Covariance Matrix with Likelihood Ratio Principle

• 발행기관: 한국자료분석학회
• 저자명: Hyo-Il Park
• 간행물 정보: 『Journal of The Korean Data Analysis Society (JKDAS)』Vol.19 No.6, 2871~2879쪽, 전체 9쪽
• 주제분류: 자연과학 > 통계학
• 파일형태: PDF
• 발행일자: 2017.12.31

영문 초록

In this study, we consider to discuss and propose a test procedure for covariance matrix under the normality assumption. For this purpose, first of all, we identify that the likelihood ratio function consists of a product of likelihood ratio functions of individual eigenvalues of covariance matrix. Then we construct a union-intersection type of statistic based on the minimum among individual p-values and propose a test. We note that the null distributions of the individual statistics are all chi-square and independent. Since the union-intersection test statistic is one of combination functions, we propose two more tests using the combination functions by combining p-values of individual partial tests. Then we compare the efficiency of the proposed tests with the asymptotic one by obtaining empirical powers through a simulation study. For this simulation study, we include the likelihood ratio test with chi-square which is the limiting distribution of the likelihood ratio statistic. Finally, we discuss some interesting features related with the test for the covariance matrix.

목차

1. Introduction

2. Tests of Covariance Matrix

3. A Numerical Example and Simulation Study

4. Some Concluding Remarks

키워드

Combination function Eigenvalue Likelihood ratio principle Multiple test Multivariate data