Exact distribution of MLE of covariance matrix in a GMANOVA-MANOVA model
For a GMANOVA-MANOVA model with normal error: Y = XB1Z1T + B2Z2T +E, E ～ Nq×n(0, In(×) ∑), the present paper is devoted to the study of distribution of MLE,Σ, of covariance matrix ∑. The main results obtained are stated as follows: (1) When rk(Z) -rk(Z2) ≥ q-rk(X), the exact distribution of (Σ) is derived, where Z = (Z1, Z2), rk(A)denotes the rank of matrix A. (2) The exact distribution of |(Σ)| is gained. (3) It is proved that ntr{[∑-1 - ∑-1XM(MTXT∑-1XM)-1MTXT∑-1]Σ} has x2(q-rk(X))(n-rk(Z2)) distribution, where M is the matrix whose columns are the standardized orthogonal eigenvectors corresponding to the nonzero eigenvalues of XT∑-1X.
作 者： BAI Peng 作者单位： Department of Statistics,University of Yunnan,Kunming 650091,China 刊 名： 中国科学A辑（英文版） SCI 英文刊名： SCIENCE IN CHINA SERIES A (MATHEMATICS) 年，卷(期)： 2005 48(12) 分类号： O1 关键词： GMANOVA-MANOVA model MLE distribution hypergeometric function