A Note on Asymptotic Normality of Kernel Estimation for Linear Random Fields on Z 2

Tsung-Lin Cheng (), Hwai-Chung Ho and Xuewen Lu
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Tsung-Lin Cheng: National Changhua University of Education
Hwai-Chung Ho: National Taiwan University
Xuewen Lu: University of Calgary

Journal of Theoretical Probability, 2008, vol. 21, issue 2, 267-286

Abstract: Abstract This note considers the kernel estimation of a linear random field on Z 2. Instead of imposing certain mixing conditions on the random fields, it is assumed that the weights of the innovations satisfy a summability property. By building a martingale decomposition based on a suitable filtration, asymptotic normality is proven for the kernel estimator of the marginal density of the random field.

Keywords: Central limit theorem; Kernel estimation; Linear random field; 60F05; 62G07 (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10959-008-0146-x

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