Weak convergence for smooth estimator of a distribution function under negative association

Authors: Zongwu Cai ^a; George G. Roussas ^b

Affiliations:	^a Department of Mathematics, University of North Carolina, Charlotte, NC
	^b Division of Statistics, University of California, Davis, CA

DOI: 10.1080/07362999908809595

Publication Frequency: 6 issues per year

Published in: journal

Stochastic Analysis and Applications, Volume 17, Issue 2 1999 , pages 145 - 168

Subjects: Statistics & Probability; Stochastic Models & Processes;

Formats available: PDF (English)

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Abstract

Let

./LSAA_A_8809595_O_XML_IMAGES/LSAA_A_8809595_O_ILM0001.gif

be real-valued random variables forming a stationary sequence, and satisfying the basic requirement of being negatively associated. Let F be the marginal distribution function of ./LSAA_A_8809595_O_XML_IMAGES/LSAA_A_8809595_O_ILM0002.gif

./LSAA_A_8809595_O_XML_IMAGES/LSAA_A_8809595_O_ILM0002.gif

which is estimated by a smooth kernel-type estimate ./LSAA_A_8809595_O_XML_IMAGES/LSAA_A_8809595_O_ILM0003.gif

, by means of the segment ./LSAA_A_8809595_O_XML_IMAGES/LSAA_A_8809595_O_ILM0004.gif

In this paper, we establish weak convergence for the smooth estimate _n

Keywords: Negative Association; Stationarity; Smooth Estimate; Tightness; Weak Convergence

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Weak convergence for smooth estimator of a distribution function under negative association

Abstract