:: Volume 6, Issue 2 (3-2010) ::
JSRI 2010, 6(2): 243-255 Back to browse issues page
Almost Sure Convergence of Kernel Bivariate Distribution Function Estimator under Negative Association
H. Jabbari Nooghabi
, Jabbarinh@um.ac.ir
Abstract:   (2676 Views)

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).

Keywords: Almost sure convergence, bivariate distribution function, kernel estimation, negative association, stationarity
Full-Text [PDF 246 kb]   (828 Downloads)    
Type of Study: Research | Subject: General
Received: 2016/01/19 | Accepted: 2016/01/19 | Published: 2016/01/19

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Volume 6, Issue 2 (3-2010) Back to browse issues page