Testing Restricted Mean Vector Under Alternatives Hypothesis

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Faijun Nahar Mim
Faijun Nahar Mim
σ
Ajit Kumar Majumder
Ajit Kumar Majumder
α Mawlana Bhashani Science and Technology University Mawlana Bhashani Science and Technology University

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Testing Restricted Mean Vector Under Alternatives Hypothesis

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Abstract

In most of the statistical models, the sign of the parameters are known is advance. In order to test the validity of the model, estimation and testing parameters to be done at the initial stage. In this case, usual unrestricted estimation and testing procedures may result in incorrect solutions. Usually, two-sided F or 2 χ testing are not suitable as well as unconstraint optimization solutions can give wrong estimate. In multivariate analysis, we usually apply two-sided Hotelling’s -2 T for testing mean vector. This test may not be appropriate for testing when an order restriction is imposed among several p-variate normal mean vector. The main objective of this paper is for a given a multivariate normal population with unknown covariance matrix to develop a new testing procedure when the mean vector slipped to the right or to the left or both. So, we proposed a new distance based one sided and partially one sided Hotelling’s -2 T to test restricted mean vectors. Monte Carlo simulations are conducted to compare power properties of the proposed 2 DT along with their respective conventional counterparts.

References

18 Cites in Article
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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Faijun Nahar Mim. 2017. \u201cTesting Restricted Mean Vector Under Alternatives Hypothesis\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 17 (GJSFR Volume 17 Issue F1): .

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Issue Cover
GJSFR Volume 17 Issue F1
Pg. 59- 67
Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords
Classification
GJSFR-F Classification: MSC 2010: 97G70
Version of record

v1.2

Issue date

February 26, 2017

Language
en
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In most of the statistical models, the sign of the parameters are known is advance. In order to test the validity of the model, estimation and testing parameters to be done at the initial stage. In this case, usual unrestricted estimation and testing procedures may result in incorrect solutions. Usually, two-sided F or 2 χ testing are not suitable as well as unconstraint optimization solutions can give wrong estimate. In multivariate analysis, we usually apply two-sided Hotelling’s -2 T for testing mean vector. This test may not be appropriate for testing when an order restriction is imposed among several p-variate normal mean vector. The main objective of this paper is for a given a multivariate normal population with unknown covariance matrix to develop a new testing procedure when the mean vector slipped to the right or to the left or both. So, we proposed a new distance based one sided and partially one sided Hotelling’s -2 T to test restricted mean vectors. Monte Carlo simulations are conducted to compare power properties of the proposed 2 DT along with their respective conventional counterparts.

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Testing Restricted Mean Vector Under Alternatives Hypothesis

Faijun Nahar Mim
Faijun Nahar Mim Mawlana Bhashani Science and Technology University
Ajit Kumar Majumder
Ajit Kumar Majumder

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