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.
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T.-L. Cheng’s research is supported in part by NSC 94-2118-M-018-001, Taiwan. Also, he is indebted to Department of Mathematics and Statistics, University of Calgary, for their hospitality during his visit. X. Lu’s research is supported in part by NSERC Discovery Grant of Canada.
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Cheng, TL., Ho, HC. & Lu, X. A Note on Asymptotic Normality of Kernel Estimation for Linear Random Fields on Z 2 . J Theor Probab 21, 267–286 (2008). https://doi.org/10.1007/s10959-008-0146-x
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DOI: https://doi.org/10.1007/s10959-008-0146-x