Hiroshima Mathematical Journal

Statistical inference for functional relationship between the specified and the remainder populations

Yasutomo Maeda

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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.

Article information

Hiroshima Math. J., Volume 40, Number 2 (2010), 215-228.

First available in Project Euclid: 2 August 2010

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Zentralblatt MATH identifier

Primary: 12A34 98B76 23C57

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


Maeda, Yasutomo. Statistical inference for functional relationship between the specified and the remainder populations. Hiroshima Math. J. 40 (2010), no. 2, 215--228. doi:10.32917/hmj/1280754422. https://projecteuclid.org/euclid.hmj/1280754422

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