%0 Journal Article
%A Jabbari Nooghabi, H.
%T Almost Sure Convergence of Kernel Bivariate Distribution Function Estimator under Negative Association
%J Journal of Statistical Research of Iran
%V 6
%N 2
%U http://jsri.srtc.ac.ir/article-1-113-en.html
%R 10.18869/acadpub.jsri.6.2.243
%D 2010
%K Almost sure convergence, bivariate distribution function, kernel estimation, negative association, stationarity,
%X Let {Xn ,n=>1} be a strictly stationary sequence of negatively associated random variables, with common distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1, Xk+1) for fixed $K /in N$ based on kernel type estimators. We introduce asymptotic normality and properties and moments. From these we derive the optimal bandwidth convergence rate, which is of order n-1. Besides of some usual conditions on the kernel function, the conditions typically impose a convenient increase rate on the covariances cov(X1,Xn).
%> http://jsri.srtc.ac.ir/article-1-113-en.pdf
%P 243-255
%& 243
%!
%9 Research
%L A-10-1-89
%+
%G eng
%@ 1735-1294
%[ 2010