Volume 5, Number 1 and 2 (November 2006)                   JIRSS 2006, 5(1 and 2): 53-67 | Back to browse issues page

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Jabbari H, Azarnoosh H A. Almost Sure Convergence Rates for the Estimation of a Covariance Operator for Negatively Associated Samples. JIRSS. 2006; 5 (1 and 2) :53-67
URL: http://jirss.irstat.ir/article-1-136-en.html

Abstract:   (5093 Views)
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.
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Subject: 60: Probability theory and stochastic processes
Received: 2011/11/4 | Accepted: 2015/09/12

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