Rational Splines with Minimax Parameters in Nonparametric Regression Inverse Problems
Pogorielov R. V. *
Taras Shevchenko National University of Kyiv, Hlushkova Avenue, 4g, 03127, Kyiv, Ukraine.
*Author to whom correspondence should be addressed.
Abstract
In this article Spath rational spline is considered as a solution to the curve-fitting problem. The parameters of the spline are recommended to be computed in accordance with the Chebyshev minimax concept. This spline does not depend on smoothing parameter and, therefore does not face with difficulties such as oversmoothing and undersmoothing. A method for creating such a spline is proposed. An application of nonparametric regression for the estimation of unknown functions in stochastic differential equations is given. A case involving a stochastic differential equation is presented, characterized by an alpha-stable process. A software application has been designed, and the associated tests have been conducted.
Keywords: Chebyshev approximation, splines, inverse problems, SDE