In a multivariate normal distribution, let the inverse of the covariance matrix be a band matrix. The distribution of the sufficient statistic for the covariance matrix is derived for this case. It is a generalization of the Wishart distribution. The distribution may be used for unbiased density estimation and construction of classification rules.

This paper investigates the continuity of projection matrices and illustrates an important application of this property to the derivation of the asymptotic distribution of quadratic forms. We give a new proof and an extension of a result of Stewart (1977).

This note contains a transparent presentation of the matrix Haffian. A basic theorem links this matrix and the differential ofthe matrix function under investigation, viz ∇F(X) and dF(X).Frequent use is being made of matrix derivatives as developed by Magnus and Neudecker.

We use Haff's fundamental identity to express the expectation of Sp in lower-order terms, where S follows the central Wishart distribution.

We complement the recently introduced classes of lower and upper semilinear copulas by two new classes, called vertical and horizontal semilinear copulas, and characterize the corresponding class of diagonals. The new copulas are in essence asymmetric, with maximum asymmetry given by $1/16$. The only symmetric members turn out to be also lower and upper semilinear copulas, namely convex sums of $\Pi$ and $M$.

The five-parameter generalized gamma distribution is one of the most flexible distributions in statistics. In this note, for the first time, we provide asymptotic covariances for the parameters using both the method of maximum likelihood and the method of moments.

Let $X_j,1\le j\le N$, be independent random $p$-vectors with respective continuous cumulative distribution functions $F_{j}1\le j\le N$. Define the $p$-vectors $R_j$ by setting $R_{ij}$ equal to the rank of $X_{ij}$ among $X_{ij},...,X_{iN},1\le i\le p,1\le j\le N$. Let $a^{\left(N\right)}(.)$ denote a multivariate score function in $R_p$, and put $S={\sum }_{j=1}^N{c}_j{a}^{\left(N\right)}\left(R_j\right)$, the $c_j$ being arbitrary regression constants. In this paper the asymptotic distribution of $S$ is investigated under various sets of conditions on the constants, the score functions, and the underlying distribution functions. In particular, asymptotic normality of $S$ is established...

By using three theorems (Oktaba and Kieloch [3]) and Theorem 2.2 (Srivastava and Khatri [4]) three results are given in formulas (2.1), (2.8) and (2.11). They present asymptotically normal confidence intervals for the determinant $|{\sigma }^2\sum |$ in the MGM model $(U,XB,{\sigma }^2\sum \otimes V)$, $\sum >0$, scalar ${\sigma }^2>0$, with a matrix $V\ge 0$. A known $n\times p$ random matrix $U$ has the expected value $E\left(U\right)=XB$, where the $n\times d$ matrix $X$ is a known matrix of an experimental design, $B$ is an unknown $d\times p$ matrix of parameters and ${\sigma }^2\sum \otimes V$ is the covariance matrix of $U,\otimes$ being the symbol of the Kronecker...