We establish certain general characterization results on elliptically symmetric distributions and exchangeable random variables. These results yield, in particular, the results given earlier by Maxwell, Bartlett, Kingman, Ali, Smith, Arnold and Lynch, and several others.

Consistent estimators for the reciprocal of the density at a quantile point, which is the derivative of the quantile function, are considered. Rates of convergence of these estimators, depending on the smoothness properties of the density, are obtained. Two different, but natural, estimators of...

We consider the linear model yi = x'i[beta] + ei, i = 1,...,n, and an estimating equation of the form [psi](y1-x'1[beta])x1 + ... + [psi](yn - x'n[beta])xn = 0 and prove the consistency of the estimator [beta] under some mild conditions on [psi]. The conditions imposed are much weaker than those...

A general solution of the Deny convolution equation restricted to a half line is obtained using certain concepts of random walk theory. The equation in question arises in several places in applied probability such as in queueing and storage theories and characterization problems of probability...

Considering a large class of tests, we study higher order power in a possibly non-iid set-up. Optimum properties for the likelihood ratio and score tests are exhibited under the criteria of second-order local maximinity and third-order local average power, respectively. The issue of stringency...