### 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.

Original language | English |
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Pages (from-to) | 53-60 |

Number of pages | 8 |

Journal | Journal of the National Science Foundation of Sri Lanka |

Volume | 44 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2016 |

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### All Science Journal Classification (ASJC) codes

- General

### Cite this

*Journal of the National Science Foundation of Sri Lanka*,

*44*(1), 53-60. https://doi.org/10.4038/jnsfsr.v44i1.7981

**On the powers of tests for homogeneity of regression coefficient vectors under synchronised order restrictions.** / Sasabuchi, Shoichi; Kulatunga, D. D.Sarath.

Research output: Contribution to journal › Article

*Journal of the National Science Foundation of Sri Lanka*, vol. 44, no. 1, pp. 53-60. https://doi.org/10.4038/jnsfsr.v44i1.7981

}

TY - JOUR

T1 - On the powers of tests for homogeneity of regression coefficient vectors under synchronised order restrictions

AU - Sasabuchi, Shoichi

AU - Kulatunga, D. D.Sarath

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84962407498&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962407498&partnerID=8YFLogxK

U2 - 10.4038/jnsfsr.v44i1.7981

DO - 10.4038/jnsfsr.v44i1.7981

M3 - Article

VL - 44

SP - 53

EP - 60

JO - Journal of the National Science Foundation of Sri Lanka

JF - Journal of the National Science Foundation of Sri Lanka

SN - 1391-4588

IS - 1

ER -