Karol Dziedziul, Piotr Paluszek (2010)
Applicationes Mathematicae
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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.
Karol Dziedziul (2001)
Applicationes Mathematicae
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We prove the central limit theorem for the integrated square error of multivariate box-spline density estimators.
Pavel Krejčíř (2000)
Kybernetika
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The problem of estimating the intensity of a non-stationary Poisson point process arises in many applications. Besides non parametric solutions, e. g. kernel estimators, parametric methods based on maximum likelihood estimation are of interest. In the present paper we have developed an approach in which the parametric function is represented by two-dimensional beta-splines.
Zbigniew Ciesielski, Ryszard Zieliński (2009)
Applicationes Mathematicae
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Dvoretzky-Kiefer-Wolfowitz type inequalities for some polynomial and spline estimators of distribution functions are constructed. Moreover, hints on the corresponding algorithms are given as well.
Jiří Kobza, Pavel Ženčák (1997)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Jitka Machalová (2002)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Jiří Kobza (1992)
Applications of Mathematics
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The extremal property of quadratic splines interpolating the first derivatives is proved. Quadratic spline smoothing the given values of the first derivative, depending on the knot weights and smoothing parameter , is then studied. The algorithm for computing appropriate parameters of such splines is given and the dependence on the smoothing parameter is mentioned.