A general method of density estimation for associated random variables

Dewan, Isha ; Prakasa Rao, B. L. S. (1999) A general method of density estimation for associated random variables Journal of Nonparametric Statistics, 10 (4). pp. 405-420. ISSN 1048-5252

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Official URL: http://www.tandfonline.com/doi/abs/10.1080/1048525...

Related URL: http://dx.doi.org/10.1080/10485259908832769

Abstract

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

Item Type:Article
Source:Copyright of this article belongs to Taylor and Francis Group.
Keywords:Density Estimation; Associated Random Variables; Uniform Consistency; Exponential Rate
ID Code:73748
Deposited On:07 Dec 2011 05:35
Last Modified:07 Dec 2011 05:35

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