Authors

• H. Jabbari
• H. A. Azarnoosh

Abstract

Let {Xn, n >= 1} be a strictly stationary sequence of negatively
associated random variables, with common continuous and
bounded distribution function F. In this paper, we consider the estimation
of the two-dimensional distribution function of (X1,Xk+1)
based on histogram type estimators as well as the estimation of the
covariance function of the limit empirical process induced by the sequence
{Xn, n>= 1}. Then, we derive uniform strong convergence
rates for two-dimensional distribution function of (X1,Xk+1) without
any condition on the covariance structure of the variables. Finally,
assuming a convenient decrease rate of the covariances
Cov(X1,Xn+1), n >= 1,
we introduce uniform strong convergence rate for covariance function
of the limit empirical process.

Keywords

• Empirical process
• histogram estimator
• negative association
• stationarity