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June 2011 LR tests for two hypotheses in profile analysis of growth curve data
Takashi Seo, Tomoko Sakurai, Yasunori Fujikoshi
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SUT J. Math. 47(2): 105-118 (June 2011). DOI: 10.55937/sut/1329739828


This paper is concerned with profile analysis of k p-dimensional normal populations Πi:Np(μi,Σ),i=1,,k, when the mean vectors are expressed as μi=Xθi,i=1,,k, where X is a p×q given matrix with rank q and θi’s are unknown parameter vectors. The model with such a mean structure is applied to growth curve data. Fujikoshi (2009) studied a likelihood ratio statistic for a parallelism hypothesis. In this paper we derive likelihood ratio statistics for level and flatness hypotheses under the parallelism hypothesis. Their null distributions are obtained. We also give an example.

Funding Statement

The first author’s research was in part supported by Grant-in-Aid for Scientific Research (C) (23500360).


The authors would like to thank Dr. M. Hyodo, The University of Tokyo, Mr. N. Shutoh, Tokyo University of Science for their help in numerical example, and also a referee for his helpful comments and careful readings.


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Takashi Seo. Tomoko Sakurai. Yasunori Fujikoshi. "LR tests for two hypotheses in profile analysis of growth curve data." SUT J. Math. 47 (2) 105 - 118, June 2011.


Received: 15 October 2010; Revised: 8 June 2011; Published: June 2011
First available in Project Euclid: 11 June 2022

Digital Object Identifier: 10.55937/sut/1329739828

Primary: 62E20 , 62H12

Keywords: Distributions of test statistics , flatness hypothesis , growth curve model , level hypothesis , likelihood ratio tests , parallelism hypothesis

Rights: Copyright © 2011 Tokyo University of Science

Vol.47 • No. 2 • June 2011
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