Unbiasedness of LRT on the homogeneity of means in MANOVA under general order restrictions
Hamdan, Mustafa; Hu, Xiaomi. 2019. Unbiasedness of LRT on the homogeneity of means in MANOVA under general order restrictions. Statistics & Probability Letters, vol. 148:pp 59-65
In this paper a likelihood ratio test is developed through matrix projections for the hypothesis on the homogeneity of mean vectors in MANOVA. It is assumed that the mean vectors are under a general multivariate order restriction. The multivariate order relation in the restriction is a generalization of orders in real numbers. Based on the study of the structure of the acceptance region with respect to a mirror image transformation, and the properties of transformed matrix distributions, the unbiasedness of the test is established.