Asymptotics of kernel density estimators on weakly associated random fields

Jia Chen

doi:10.1016/j.spl.2008.06.024

Asymptotics of kernel density estimators on weakly associated random fields

Jia Chen

Economics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	3230–3237
Number of pages	8
Journal	Statistics & Probability Letters
Volume	78
Issue number	18
Early online date	21 Jun 2008
DOIs	https://doi.org/10.1016/j.spl.2008.06.024
Publication status	Published - 15 Dec 2008

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10.1016/j.spl.2008.06.024

Cite this

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title = "Asymptotics of kernel density estimators on weakly associated random fields",

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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AB - 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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