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• W2016013506 abstract "Abstract Nonparametric estimation for an unknown probability density function f with a known compact support [0, 1] not necessarily bounded at x=0 is considered. For such class of density functions, we consider the Bernstein estimator. The uniform weak consistency and the uniform strong consistency on each compact I in (0, 1) are established for the Bernstein estimator. We prove also the almost sure convergence to infinity at x=0 of the Bernstein estimator when the density function f is unbounded at x=0. To select the optimal bandwidth parameter of the Bernstein estimator, the least squares cross-validation and the likelihood cross-validation methods are developed. Keywords: Density estimationBernstein polynomialUnbounded densityWeak consistency Acknowledgements Comments by Ingrid Van Keilegom are gratefully acknowledged; they have been most useful for the improvement of the exposition. Support from the contract “Projet d’Actions de Recherche Concertées” n 0 98/03−217, and from the IAP research network n 0P5/24 of the Belgian state are also gratefully acknowledged." @default.
• W2016013506 created "2016-06-24" @default.
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• W2016013506 date "2007-04-01" @default.
• W2016013506 modified "2023-10-01" @default.
• W2016013506 title "Bernstein estimator for unbounded density function" @default.
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• W2016013506 doi "https://doi.org/10.1080/10485250701441218" @default.
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