排序方式: 共有4条查询结果,搜索用时 15 毫秒
1
1.
Power studies of tests of equality of covariance matrices of two p-variate complex normal populations σ1 = σ2 against two-sided alternatives have been made based on the following five criteria: (1) Roy's largest root, (2) Hotelling's trace, (4) Wilks' criterion and (5) Roy's largest and smallest roots. Some theorems on transformations and Jacobians in the two-sample complex Gaussian case have been proved in order to obtain a general theorem for establishing the local unbiasedness conditions connecting the two critical values for tests (1)–(5). Extensive unbiased power tabulations have been made for p=2, for various values of n1, n2, λ1 and λ2 where n1 is the df of the SP matrix from the ith sample and λ1 is the ith latent root of σ1σ-12 (i=1, 2). Equal tail areas approach has also been used further to compute powers of tests (1)–(4) for p=2 for studying the bias and facilitating comparisons with powers in the unbiased case. The inferences have been found similar to those in the real case. (Chu and Pillai, Ann. Inst. Statist. Math. 31. 相似文献
2.
This paper proposes the density and characteristic functions of a general matrix quadratic form X(?)AX, when A=A(?) is a positive semidefinite matrix, X has a matrix multivariate elliptical distribution and X(?) denotes the usual conjugate transpose of X. These results are obtained for real normed division algebras. With particular cases we obtained the density and characteristic functions of matrix quadratic forms for matrix multivariate normal, Pearson type VII, t and Cauchy distributions. 相似文献
3.
A general procedure for obtaining matrix derivatives of functions of nonlinear patterned matrices is proposed. The method is extended to obtain the Jacobians of patterned matrix transformations. Nel (1980) and Wiens (1985) consider the linear patterned cases. The procedure proposed here takes care of these cases as well. 相似文献
4.
The vec of a matrix X stacks columns of X one under another in a single column; the vech of a square matrix X does the same thing but starting each column at its diagonal element. The Jacobian of a one-to-one transformation X → Y is then ∣∣?(vecX)/?(vecY) ∣∣ when X and Y each have functionally independent elements; it is ∣∣ ?(vechX)/?(vechY) ∣∣ when X and Y are symmetric; and there is a general form for when X and Y are other patterned matrices. Kronecker product properties of vec(ABC) permit easy evaluation of this determinant in many cases. The vec and vech operators are also very convenient in developing results in multivariate statistics. 相似文献
1