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Bernstein-type operators on the half line

Antonio Attalienti, Michele Campiti (2002)

Czechoslovak Mathematical Journal

We define Bernstein-type operators on the half line [ 0 , + [ by means of two sequences of strictly positive real numbers. After studying their approximation properties, we also establish a Voronovskaja-type result with respect to a suitable weighted norm.

Box-spline histograms for multivariate density estimation

Karol Dziedziul, Piotr Paluszek (2010)

Applicationes Mathematicae

The uniform approach to calculation of MISE for histogram and density box-spline estimators gives us a possibility to obtain estimators of derivatives of densities and the asymptotic constant.

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