Unlike the usual stochastic order, total positivity order is closed under conditioning. Here we provide a general formulation of the preservation properties of the order under conditioning; we study certain properties of the order including translation properties and the implications of having...

The tails of the distribution of a mean zero, variance σ2 random variable Y satisfy concentration of measure inequalities of the form P(Y≥t)≤exp(−B(t)) forB(t)=t22(σ2+ct)for  t≥0,andB(t)=tc(logt−loglogt−σ2c)for  te whenever there exists a zero biased coupling of Y bounded by c,...

The Robbins-Monro procedure is investigated for various choices of step sizes, including those of the form c / nlog n, c 0. Rates of convergence using this and other choices are compared to rates obtained using cn[beta], for . Of all choices considered, it is seen that a procedure of Fabian's...

Efficiencies of the maximum pseudolikelihood estimator and a number of related estimators for the case-cohort sampling design in the proportional hazards regression model are studied. The asymptotic information and lower bound for estimating the parametric regression parameter are calculated...

A concentration of measure result is proved for the number of isolated vertices Y in the Erdos-Rényi random graph model on n edges with edge probability p. When [mu] and [sigma]2 denote the mean and variance of Y respectively, P((Y-[mu])/[sigma]=t) admits a bound of the form e-kt2 for some...

The moments of certain stochastic integrals with respect to Brownian motion are well known. In this paper the mean and variance of some integrals involving Brownian bridges are found.

This paper concerns the rate of convergence in the central limit theorem for certain local dependence structures. The main goal of the paper is to obtain estimates of the rate in the multidimensional case. Certain one-dimensional results are also improved by using some more flexible...