An estimator is said to be of orders0 if its bias has magnitude n−s, where n is the sample size. We give delta estimators and jackknife estimators of order four for smooth functions of the parameters of a multinomial distribution. An unbiased estimator is given for its density function. We...

The recent paper by Alshabani et al. [Partial size-and-shape distributions, J. Multivariate Anal. (2006), in press] derived the partial size-and-shape distributions motivated by a study in human movement analysis. The paper contained three main results (referred to as Results 1-3), each deriving...

Mehler gave an expansion for the standard bivariate normal density. Kibble extended it to a multivariate normal density whose covariance is a correlation matrix. We give extensions of these expansions for general covariances.

The distributions of the ratio X/Y are derived when (X,Y) has the elliptically symmetric Pearson-type II distribution, elliptically symmetric Pearson-type VII distribution and the elliptically symmetric Kotz-type distribution.

Edgeworth-type expansions are given for the distribution of (normalized versions of) the amplitude and phase of the mean of a sample of complex random variables. These expansions are transformed to polar forms with applications to modeling signals from a cell-phone. Limiting distributions of...

We summarize the main results known for the complex normal and complex Wishart, then give the cumulants of the central and noncentral complex Wishart. Their moments are expressed explicitly in terms of multivariate Bell polynomials, believed to be used here for the first time. Multivariate Bell...

We give formulas for the conditional expectations of a product of multivariate Hermite polynomials with multivariate normal arguments. These results are extended to include conditional expectations of a product of linear combination of multivariate normals. A unified approach is given that...