Shanbag gave a characterization of the exponential and geometric distribution in terms of conditional expectations. Recently, Kotlarski generalized his method to obtain some properties of univariate probability distributions through conditional expectations. A property of bivariate distributions...

The rate of convergence of the least squares estimator in a non-linear regression model with errors forming either a [phi]-mixing or strong mixing process is obtained. Strong consistency of the least squares estimator is obtained as a corollary.

The asymptotic properties of the least squares estimator of the cusp in some nonlinear nonregular regression models is investigated via the study of the weak convergence of the least squares process generalizing earlier results in Prakasa Rao (Statist. Probab. Lett. 3 (1985) 15).

Motivated by problems in molecular biosciences wherein the evaluation of entropy of a molecular system is important for understanding its thermodynamic properties, we consider the efficient estimation of entropy of a multivariate normal distribution having unknown mean vector and covariance...