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Density estimation for samples satisfying a certain absolute regularity condition
Authors:Ken-ichi Yoshihara
Affiliation:Department of Mathematics, Faculty of Engineering, Yokohama National University, 156 Tokiwadai, Hodogaya-ku, Yokohama, Japan
Abstract:
Let {ξi} be an absolutely regular sequence of identically distributed random variables having common density function f(x). Let Hk(x,y) (k=1, 2,…) be a sequence of Borel-measurable functions and fn(x)=n?1(Hn(x,ξ1)+…+Hn(x,ξn)) the empirical density function. In this paper, the asymptotic property of the probability P(supx|fn(x)?f(x)|>ε) (n→∞) is studied.
Keywords:Density estimation  Absolutely regular  Empirical density function  Borel-measurable function
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