Vijay K. Rohatgi

On multivariate skewness and kurtosis

Let X be a d-dimensional standardized random variable

Sharp inequalities between skewness and kurtosis

({\bf E}(X) = 0, \operatorname{cov} (X) = 1)

Distribution of order statistics with random sample size

. Then for a multivariate analogue of skewness

Small sample and efficiency results for the Nelson-Aalen estimator

s = {\bf E}(\| X \|^2 X)

A class of distributions connected to order statistics with nonintegral sample size

and kurtosis

On the estimation of restricted mean

k = {\bf E}XX^T XX^T - (d + 2)I

Shrinkage estimation of the proportion in randomized response

we show that

On the non-existence of ancillary statistics

\| s \|^2 \leqq {\text{tr}}\, k + 2d

Minimum variance unbiased estmation in some nonregulr families

. For infinitely divisible distributions

Unbiased estimation in type II censored samples from a one-truncation parameter density

\| s \|^2 \leqq {\text{tr }}k