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.
Ciesielski, Zbigniew, Kamont, Anna (1999)
Mathematica Pannonica
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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.
R. Zejnullahu (1989)
Matematički Vesnik
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Branga, Adrian (1996)
General Mathematics
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Segeth, Karel
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Spline theory is mainly grounded on two approaches: the algebraic one (where splines are understood as piecewise smooth functions) and the variational one (where splines are obtained via minimization of quadratic functionals with constraints). We show that the general variational approach called smooth interpolation introduced by Talmi and Gilat covers not only the cubic spline but also the well known tension spline (called also spline in tension or spline with tension). We present the...
Stojanović, Mirjana (1988)
Publications de l'Institut Mathématique. Nouvelle Série
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Mirjana Stojanović (1988)
Publications de l'Institut Mathématique
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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.
Jiří Kobza, Jan Mlčák (1994)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Vladimir Bogdanov, Wladimir Karsten, Valeriy Miroshnichenko, Yuriy Volkov (2013)
Open Mathematics
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A method for solving the inverse kinematic problem of determining the velocity characteristic of a medium from a vertical seismic survey, is proposed. It is based on the combined use of the eikonal equation and spline methods of approximation for multivariable functions. The problem is solved by assuming a horizontally stratified medium; no assumptions about the number of layers and their thickness are made. First, using the data of the first arrival times of the seismic signal from...