A Simultaneous Inference for the Multivariate Data

• 발행기관: 한국자료분석학회
• 저자명: Hyo-Il Park
• 간행물 정보: 『Journal of The Korean Data Analysis Society (JKDAS)』Vol.19 No.2, 557~564쪽, 전체 8쪽
• 주제분류: 자연과학 > 통계학
• 파일형태: PDF
• 발행일자: 2017.04.30

영문 초록

In this paper, we consider to propose several simultaneous tests for the mean vector and covariance matrix under the multivariate normality assumption for the underlying distribution. For doing this purpose, we consider to apply the likelihood ratio principle to obtain optimal test statistics in an optimal sense. Then we factor out two types of statistics from the likelihood ratio statistic and identify them a product two individual likelihood ratio test statistics such that one is for the test of the mean vector, the other, that of the covariance matrix. Since it would be difficult to obtain the joint distribution of the two types of the individual statistics, we consider to use the combination functions which combine the -values from the individual partial hypothesis test results. Then we derive the distributions for the combination functions under the null hypothesis. Also we illustrate our test procedure with a numerical bivariate example which is obtained for the measurement of head sizes for the first and second sons and compare their results based on the p-values. Then we discuss some interesting features our proposed simultaneous tests with some related topics. Finally we allude some future topics with simultaneous test procedure with covariance matrix.

목차

1. Introduction

2. Simultaneous Tests

3. An Example and some Concluding Remarks

키워드

Combination function Likelihood ratio test Multivariate normal distribution Simultaneous test