Optimal bandwidth selection for multivariate kernel deconvolution density estimation |
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Authors: | Élie Youndjé Martin T Wells |
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Affiliation: | 1.Laboratoire de Mathématiques Rapha?l Salem,Université de Rouen,Saint Etienne du Rouvray,France;2.Department of Social Statistics,Cornell University,Ithaca,USA |
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Abstract: | Assume we have i.i.d. replications from the mismeasured random vector Y=X+ε, where X and ε are mutually independent. We consider a data-driven bandwidth, based on a cross-validation ideas, for multivariate kernel
deconvolution estimator of the density of X. The proposed data-driven bandwidth selection method is shown to be asymptotically optimal. As a by-product of the proof
of this result, we show that the average squared error, the integrated squared error, and the mean integrated squared error
are asymptotically equivalent error measures.
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Keywords: | Density estimation Deconvolution Cross-validation Asymptotic optimality |
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