Let A1, A2, ..., An and B1, B2, ..., BN be two sequences of events. Let mn(A) and mN(B) be the number of those Aj and Bk, respectively, which occur. Set Sk,t for the joint (k, t)th binomial moment of the vector (mn(A),mN(B)). We prove that linear bounds in terms of the Sk,t on the distribution...

The lattice conditional independence (LCI) model N() is defined to be the set of all normal distributions N(0, [Sigma]) on I such that for every pair L, M [set membership, variant] , xL and xM are conditionally independent given xL [intersection] M. Here is a ring of subsets (hence a...

Given the simple linear regression model Yi = [alpha] + [beta]Xi + ei for i = 1, ..., n, we consider the repeated median estimator of the intercept [alpha], defined as [alpha]n = medi medj,j [not equal to] i (XjYi - XiYj)/(Xj - Xi). We determine the influence function and prove asymptotic...

In this paper, a representation due to Major and Rejtö for the Kaplan-Meier estimator is applied to establish a Bahadur representation for the kernel quantile estimator under random censorship. Comparing it with the product-limit quantile estimator, the convergence rate of the remainder term is...

A stronger result on the limiting distribution of the eigenvalues of random Hermitian matrices of the form A + XTX*, originally studied in Marcenko and Pastur, is presented. Here, X(N - n), T(n - n), and A(N - N) are independent, with X containing i.i.d. entries having finite second moments, T...

We construct a conservative error reporting function for the accuracy of M-estimators of a multi-dimensional statistical parameter in the context of a fixed finite number of independent but not identically distributed observations. The requirement that error estimates be conservative has been...

This paper deals with the first order Edgeworth expansions for sums related to an ergodic Markov chain with general state space. In the first part of the paper, we establish certain continuity, w.r.t. the transition probability function and the initial distribution, in these expansions. In the...

A stochastic integral representation is obtained for unitary operators induced by a class of flows of diffeomorphisms of a smooth manifold which are driven by stochastic processes with stationary and independent increments.

The class of all possible distribution functions of each order statistic for a sample of possibly dependent, identically distributed random variables is characterized. An effective method of determination of the extreme values for the expectation and variance of an arbitrary Borel function of...

This paper discusses estimation of the semilinear model E[y x, z] = x'[beta] + g(z) using series approximations to the unknown function g(z) under much weaker conditions than heretofore given in the literature. In particular, we allow for z being multidimensional and to have a discrete...