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On the powers of tests for homogeneity of regression coefficient vectors under synchronised order restrictions

Authors:

Shoichi Sasabuchi,

JP
About Shoichi

Department of Environment Design, Faculty of Design, Kyushu University, 4-9-1, Shiobaru, Minami-ku, Fukuoka-shi, 815-8540, Japan.

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DD Sarath Kulatunga

LK
About DD Sarath

Deaprtment of Mathematics, Faculty of Science, University of Kelaniya, Kelaniya.

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Abstract

We consider a multivariate multiple linear regression model and study the problem of testing homogeneity of regression coefficient vectors under synchronised order restrictions when the covariance matrices are common but unknown. Synchronised order restrictions are the generalisation of the multivariate isotonic order restrictions. Synchronised order restricted test could be applied to a situation where the values of some parameters increase, those of some other parameters decrease, and those of the rest of the parameters have no restriction, simultaneously. For this problem, some test statistics were proposed and some inequalities among their powers were obtained in the past. This showed that the proposed test statistics may equally be good in terms of their powers. In the present paper, we mathematically prove that the strict inequalities hold among the powers of the test statistics. Thus we attain an exact comparison among the powers of the test statistics indicating more accurate and stronger results than those obtained in the past.
How to Cite: Sasabuchi, S. and Kulatunga, D.S., 2016. On the powers of tests for homogeneity of regression coefficient vectors under synchronised order restrictions. Journal of the National Science Foundation of Sri Lanka, 44(1), pp.53–60. DOI: http://doi.org/10.4038/jnsfsr.v44i1.7981
Published on 31 Mar 2016.
Peer Reviewed

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