Let X1,X2,... be real-valued random variables forming a strictly stationary sequence, and satisfying the basic requirement of being positively or negatively associated. Let [xi]p denote the pth quantile of the marginal distribution function of the Xi's, which is estimated by a smooth...

Let s{;Xns};, n [greater-or-equal, slanted] 1, be a stationary [alpha]-mixing sequence of real-valued r.v.'s with distribution function (d.f.) F, probability density function (p.d.f.) f and mixing coefficient [alpha](n). The d.f. F is estimated by the empirical d.f. Fn, based on the segment...

For n = 1, 2,... and i integer between 1 and n, let xni be fixed design points in a compact subset S of , and let Yni be observations taken at these points through g, an unknown continuous real-valued function defined on , and subject to errors [var epsilon]ni; that is, Yni = g(xni) + [var...

The sole purpose of this paper is to establish asymptotic normality of the usual kernel estimate of the marginal probability density function of a strictly stationary sequence of associated random variables. In much of the discussions and derivations, the term association is used to include both...

Let X1, X2,..., Xn be p-dimensional random vectors coming from a strictly stationary sequence which is also subject to any one of the four standard kinds of mixing. The survival function is defined by (x) = P(X x), where X is distributed as the X's above and the inequality X x is to be...

In this note, an upper bound is provided for the supremum of the absolute value of the difference of the probability density functions of two k-dimensional random vectors. The bound involves integrals of the absolute value of the characteristic functions of the random vectors, and shares a...

Sharp convergence rates for fixed design regression estimators for negatively associated random variables are established. The rates are obtained by means of exponential inequalities, which hold under general conditions.

Let X1,..., Xn + 1 be the first n + 1 random variables from a strictly stationary Markov process which satisfies certain additional regularity conditions. On the basis of these random variables, a recursive nonparametric estimate of the one-step transition distribution function is shown to be...