Title : ( Almost sure convergence of kernel bivariate distribution function estimator under negative association )
Authors: Hadi Jabbari Nooghabi ,
Full TextAbstract
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 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
, MSC 2000: Primary 62G20; Secondary 60F15, 62N05. keywords: Almost sure convergence, Bivariate distribution function, Kernel estimation, Negatively association, Stationarity.
@inproceedings{paperid:1013127,
author = {Jabbari Nooghabi, Hadi},
title = {Almost sure convergence of kernel bivariate distribution function estimator under negative association},
booktitle = {The 7th Seminar on Probability and Stochastic Processes},
year = {2009},
location = {اصفهان, IRAN},
keywords = {MSC 2000: Primary 62G20; Secondary 60F15; 62N05.
keywords: Almost sure convergence; Bivariate distribution function; Kernel estimation; Negatively
association; Stationarity.},
}
%0 Conference Proceedings
%T Almost sure convergence of kernel bivariate distribution function estimator under negative association
%A Jabbari Nooghabi, Hadi
%J The 7th Seminar on Probability and Stochastic Processes
%D 2009
