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13.363 Articles in journals published by the UPC
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Asymptotic normality of the integrated square error of a density estimator in the convolution model

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Butucea, Cristina
Document typeArticle
Defense date2004
PublisherInstitut d'Estadística de Catalunya
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 2.5 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 2.5 Spain
Abstract
In this paper we consider a kernel estimator of a density in a convolution model and give a central limit theorem for its integrated square error (ISE). The kernel estimator is rather classical in minimax theory when the underlying density is recovered from noisy observations. The kernel is fixed and depends heavily on the distribution of the noise, supposed entirely known. The bandwidth is not fixed, the results hold for any sequence of bandwidths decreasing to 0. In particular the central limit theorem holds for the bandwidth minimizing the mean integrated square error (MISE). Rates of convergence are sensibly different in the case of regular noise and of super-regular noise. The smoothness of the underlying unknown density is relevant for the evaluation of the MISE.
CitationButucea, Cristina. "Asymptotic normality of the integrated square error of a density estimator in the convolution model". SORT, 2004, Vol. 28, núm. 1 
URIhttp://hdl.handle.net/2099/3747
ISSN1696-2281
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  • SORT (Statistics and Operations Research Transactions) - 2004, Vol. 28, Núm. 1 [7]
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