Suppose that {Xi; I = 1, 2, ...,} is a sequence of p-dimensional random vectors forming a stochastic process. Let pn, [theta](Xn), Xn [set membership, variant] np, be the probability density function of Xn = (X1, ..., Xn) depending on [theta] [set membership, variant] [Theta], where [Theta] is...

The set of the functions H, which are limiting distributions of linearly normalized maxima of n independent and identically distributed random vectors, is treated. It is shown that there is a connection between Pickands' representation for H and the one given by D. G. Kendall for the p-function...

We establish a version of the maximal inequality for multiparameter stochastic processes with independent increments taking values in T0 topological Abelian groups. As an application of this inequality, we prove the existence of a modification without discontinuities of the second kind for a...

Three classes of expansions for the distribution function of the [chi]k2(d, R)-distribution are given, where k denotes the dimension, d the degree of freedom, and R the "accompanying correlation matrix." The first class generalizes the orthogonal series with generalized Laguerre polynomials,...

We investigate conditions under which estimators of the form X + aU'Ug(X) dominate X when X, a p - 1 vector, and U, an m - 1 vector, are distributed such that [X1, X2,..., Xp, U1, U2,..., Up]'/[sigma] has a spherically symmetric distribution about [[theta]1, [theta]2,..., [theta]p, 0, 0,...,...

Let X1, ..., Xn be a sequence of independent [0, 1]-valued random variables and let 0 [beta] = 1. A complete comparison is made between the optimal stopping value V(X1, [beta]X2, ..., [beta]n-1Xn) = sup{E[beta][tau]-1X[tau]: [tau] is a stop rule for X1, ..., Xn} and E(max1=i=n[beta]i-1Xi). In...

In this paper a new form of multivariate gamma is defined whose components are positively correlated and have a three parameter gamma distribution. Explicit forms of moments, moment generating function, conditional moments, and density representations are derived. Several properties of the...

We show that the coverage error of confidence intervals and level error of hypothesis tests for population quantiles constructed using the bootstrap estimate of sample quantile variance is of precise order n-1/2 in both one- and two-sided cases. This contrasts markedly with more classical...

This paper establishes a central limit theorem (CLT) for empirical processes indexed by smooth functions. The underlying random variables may be temporally dependent and non-identically distributed. In particular, the CLT holds for near epoch dependent (i.e., functions of mixing processes)...

Suppose you observe a finite sequence of random variables from some known joint distribution F, you can stop the process at any time and your profit is the last observed value. If an optimal stopping rule is used, denote the expected profit by VF. What kind of ordering on multivariate...