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Asymptotic normality of the integrated square error of a density estimator in the convolution model
Butucea, Cristina (Université de Paris)

Data: 2004
Resum: 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.
Drets: Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades. Creative Commons
Llengua: Anglès
Document: article ; recerca ; publishedVersion
Matèria: Convolution density estimation ; Nonparametric density estimation ; Central limit theorem ; Integrated squared error ; Noisy observations
Publicat a: SORT : statistics and operations research transactions, Vol. 28, Núm. 1 (January-June 2004) , p. 9-26, ISSN 1696-2281

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