A New Test for Multivariate Ordered Alternatives: Medical Application and Geometric Interpretation

Abouzar Bazyari, Mahmoud Afshari

Abstract


In the present paper, the geometric interpretation and medical application of ordered one-sided hypothesis testing are presented. We consider tests for the hypothesis that the mean vectors are zero against one-sided alternatives when the observation vectors are independently and identically distributed as normal with known and unknown covariance matrices. This problem is an extension of Kudo (1963) and Glimm et al. (2002) to several multivariate normal distributions. When the covariance matrices are known, the test statistic is derived and we give suitable conditions which under the one-sided restricted alternative hypothesis the obtained estimator is the maximum likelihood estimate. We shall discuss a geometric interpretation of the test statistic based on the closed convex polyhedral cone and also obtain its null distribution in the special case. Also, when the covariance matrices are unknown and common a proper test statistic is proposed. To evaluate the results, the effect of a drug is investigated on the body of one-day babies for suspected Sepsis disease.


Keywords


Geometric interpretation; Medical application; Ordered mean vectors; Polyhedral cone; Sepsis disease.

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DOI: http://dx.doi.org/10.18187/pjsor.v14i3.2178

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Title

A New Test for Multivariate Ordered Alternatives: Medical Application and Geometric Interpretation

Keywords

Geometric interpretation; Medical application; Ordered mean vectors; Polyhedral cone; Sepsis disease.

Description

In the present paper, the geometric interpretation and medical application of ordered one-sided hypothesis testing are presented. We consider tests for the hypothesis that the mean vectors are zero against one-sided alternatives when the observation vectors are independently and identically distributed as normal with known and unknown covariance matrices. This problem is an extension of Kudo (1963) and Glimm et al. (2002) to several multivariate normal distributions. When the covariance matrices are known, the test statistic is derived and we give suitable conditions which under the one-sided restricted alternative hypothesis the obtained estimator is the maximum likelihood estimate. We shall discuss a geometric interpretation of the test statistic based on the closed convex polyhedral cone and also obtain its null distribution in the special case. Also, when the covariance matrices are unknown and common a proper test statistic is proposed. To evaluate the results, the effect of a drug is investigated on the body of one-day babies for suspected Sepsis disease.


Date

2018-09-22

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 14 No. 3, 2018



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810