Statistical inference for functional relationship between the specified and the remainder populations
Maeda, Yasutomo
Hiroshima Math. J., Tome 40 (2010) no. 1, p. 215-228 / Harvested from Project Euclid
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.
Publié le : 2010-07-15
Classification:  asymptotic distribution,  high-dimensional framework,  likelihood ratio test statistics (LR test statistics),  linear functional relationship,  maximum likelihood estimators (MLE),  12A34,  98B76,  23C57
@article{1280754422,
     author = {Maeda, Yasutomo},
     title = {Statistical inference for functional relationship between the specified and the
				remainder populations},
     journal = {Hiroshima Math. J.},
     volume = {40},
     number = {1},
     year = {2010},
     pages = { 215-228},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1280754422}
}
Maeda, Yasutomo. Statistical inference for functional relationship between the specified and the
				remainder populations. Hiroshima Math. J., Tome 40 (2010) no. 1, pp.  215-228. http://gdmltest.u-ga.fr/item/1280754422/