This paper considers a flexible class of omnibus affine invariant tests for the hypothesis that a multivariate distribution is symmetric about an unspecified point. The test statistics are weighted integrals involving the imaginary part of the empirical characteristic function of suitably...

Let X,X1,...,Xm,..., Y,Y1,...,Yn,... be independent d-dimensional random vectors, where the Xj are i.i.d. copies of X, and the Yk are i.i.d. copies of Y. We study a class of consistent tests for the hypothesis that Y has the same distribution as X+[mu] for some unspecified . The test statistic L...

We derive the asymptotic distributions for measures of multivariate skewness and kurtosis defined by Malkovich and Afifi if the underlying distribution is elliptically symmetric. A key step in the derivation is an approximation by suitable Gaussian processes defined on the surface of the unit...

We consider the problem of estimating the eigenvalues of noncentrality parameter matrix in noncentral Wishart distribution when the scale parameter is known. A decision theoretic approach is taken with squared error as the loss function. We propose two new estimators and show their superior...

In this paper some characterization results ofLp-norm spherical distributions are obtained. It is proved that ifX=(X1, ..., Xn)' has aLp-norm spherical distribution having certain independence properties, thenX1, X2, ..., Xnmust be i.i.d. with p.d.f.p(x)[is proportional to]e-xp/c....

In this paper, it is shown that two random matrices have a joint matrix variate normal distribution if, conditioning each one on the other, the resulting distributions satisfy certain conditions. A general result involving more than two matrices is also proved.

Phillips (J. Multivariate Anal. 16 (1985) 157) generalizes Cramer's (Mathematical Methods of Statistics, Princeton University Press, Princeton, NJ, 1946) inversion formula for the distribution of a quotient of two scalar random variables to the matrix quotient case. However, he gives the result...

In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and...