Journal of the Iranian Statistical Society, Volume (5), No (1), Year (2006-8) , Pages (57-67)

Title : ( Almost sure convergence rates for the estimation of a covariance operator for negatively associated samples )

Authors: Hadi Jabbari Nooghabi ,

Citation: BibTeX | EndNote

Let {Xn, n  1} be a strictly sationary 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,
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@article{paperid:1006560,
author = {Jabbari Nooghabi, Hadi},
title = {Almost sure convergence rates for the estimation of a covariance operator for negatively associated samples},
journal = {Journal of the Iranian Statistical Society},
year = {2006},
volume = {5},
number = {1},
month = {August},
issn = {1726-4057},
pages = {57--67},
numpages = {10},
keywords = {Empirical process; histogram estimator; negative association; stationarity.},
}

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%0 Journal Article
%T Almost sure convergence rates for the estimation of a covariance operator for negatively associated samples
%A Jabbari Nooghabi, Hadi
%J Journal of the Iranian Statistical Society
%@ 1726-4057
%D 2006

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