Journal of Probability and Statistical Science, Volume (6), No (1), Year (2008-2) , Pages (39-51)

Title : ( A General Method of Density Estimation for Negatively Associated Random Variables )

Authors: Hadi Jabbari Nooghabi ,

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Let be a stationary sequence of negatively associated random variables having a common marginal density function f(x). Let {X n , n ≥ 1} (x, y), n ψ n = 1, 2, L be a sequence of Borel-measurable functions defined on R2 . Let be the empirical density function. Here we study a set of sufficient conditions under which the probability fn (x) = Σ = n n k n x Xk 1 (1/ ) ψ ( , ) {sup | ( ) − ( ) | > } → 0 + ≤ ≤ − ε P a δ x b δ fn x f x at an exponential rate as n → ∞ , where the rate possibly depends on ε , δ and f and [a, b] is a finite interval.

Keywords

Density function; Exponential rate; Negative association; Uniform consistency. (AMS 2000:
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@article{paperid:1006561,
author = {Jabbari Nooghabi, Hadi},
title = {A General Method of Density Estimation for Negatively Associated Random Variables},
journal = {Journal of Probability and Statistical Science},
year = {2008},
volume = {6},
number = {1},
month = {February},
issn = {1726-3328},
pages = {39--51},
numpages = {12},
keywords = {Density function; Exponential rate; Negative association; Uniform consistency. (AMS 2000: 60F15)},
}

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%0 Journal Article
%T A General Method of Density Estimation for Negatively Associated Random Variables
%A Jabbari Nooghabi, Hadi
%J Journal of Probability and Statistical Science
%@ 1726-3328
%D 2008

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