The 9th Seminar on Probability and Stochastic Processes , 2013-09-11

Title : ( On almost sure convergence rates for the Kernel estimation of a covariance operator under negative association )

Authors: Hadi Jabbari Nooghabi , M. Erfaniyan , B. Ghanbari ,

Citation: BibTeX | EndNote

Let fXn; n  1g be a strictly stationary sequence of negatively associated ran- dom 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 Kernel type estimators as well as the estimation of the covariance function of the limit empirical process induced by the sequence fXn; n  1g. Then, we derive uniform strong convergence rates for the Kernel estimator of two-dimensional distribution function of (X1;Xk+1) which were not found already and do not need any conditions 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 based on Kernel type estimators.

Keywords

, Almost sure convergence rate, Bivariate distribution function, Empirical process, Kernel
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@inproceedings{paperid:1036155,
author = {Jabbari Nooghabi, Hadi and M. Erfaniyan and B. Ghanbari},
title = {On almost sure convergence rates for the Kernel estimation of a covariance operator under negative association},
booktitle = {The 9th Seminar on Probability and Stochastic Processes},
year = {2013},
location = {زاهدان, IRAN},
keywords = {Almost sure convergence rate; Bivariate distribution function; Empirical process; Kernel estimation.},
}

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%0 Conference Proceedings
%T On almost sure convergence rates for the Kernel estimation of a covariance operator under negative association
%A Jabbari Nooghabi, Hadi
%A M. Erfaniyan
%A B. Ghanbari
%J The 9th Seminar on Probability and Stochastic Processes
%D 2013

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