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Asymptotics of kernel density estimators on weakly associated random fields

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JournalStatistics & Probability Letters
DateE-pub ahead of print - 21 Jun 2008
DatePublished (current) - 15 Dec 2008
Issue number18
Volume78
Number of pages8
Pages (from-to)3230–3237
Early online date21/06/08
Original languageEnglish

Abstract

Let ZNZN, N≥1N≥1 denote the integer lattice points in the NN-dimensional Euclidean space and View the MathML source{Xn} be an RdRd-valued, strictly stationary, weakly associated random field indexed by ZNZN. Under mild conditions, as in [Roussas, G.G., 2000. Asymptotic normality of the kernel estimate of a probability density function under association. Statist. Probab. Lett. 50, 1–12], asymptotic normality of the kernel estimator of the multivariate density is established. We also investigate the mean squared error of the estimator towards the unknown density.

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