## Hiroshima Mathematical Journal

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

Yasutomo Maeda

#### Abstract

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

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

Dates
First available in Project Euclid: 2 August 2010

https://projecteuclid.org/euclid.hmj/1280754422

Digital Object Identifier
doi:10.32917/hmj/1280754422

Mathematical Reviews number (MathSciNet)
MR2680657

Zentralblatt MATH identifier
1284.62140

Subjects
Primary: 12A34 98B76 23C57

#### Citation

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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