Open Access
July 2010 Statistical inference for functional relationship between the specified and the remainder populations
Yasutomo Maeda
Hiroshima Math. J. 40(2): 215-228 (July 2010). DOI: 10.32917/hmj/1280754422


This paper is concerned with discovering linear functional relationships among $k$ $p$-variate populations with mean vectors $\vmu_{i}$, $i=1,\ldots ,k$ and a common covariance matrix $\Sigma$. We consider a linear functional relationship to be one in which each of the specified $r$ mean vectors, for example, $\vmu_{1}, \ldots, \vmu_{r}$ are expressed as linear functions of the remainder mean vectors $\vmu_{r+1}, \ldots, \vmu_{k}$. This definition differs from the classical linear functional relationship, originally studied by Anderson [1], Fujikoshi [8] and others, in that there are $r$ linear relationships among $k$ mean vectors without any specification of $k$ populations. To derive our linear functional relationship, we first obtain a likelihood test statistic when the covariance matrix $\Sigma$ is known. Second, the asymptotic distribution of the test statistic is studied in a high-dimensional framework. Its accuracy is examined by simulation.


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Yasutomo Maeda. "Statistical inference for functional relationship between the specified and the remainder populations." Hiroshima Math. J. 40 (2) 215 - 228, July 2010.


Published: July 2010
First available in Project Euclid: 2 August 2010

zbMATH: 1284.62140
MathSciNet: MR2680657
Digital Object Identifier: 10.32917/hmj/1280754422

Primary: 12A34 , 23C57 , 98B76

Keywords: asymptotic distribution , high-dimensional framework , likelihood ratio test statistics (LR test statistics) , linear functional relationship , maximum likelihood estimators (MLE)

Rights: Copyright © 2010 Hiroshima University, Mathematics Program

Vol.40 • No. 2 • July 2010
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