DM-Artículos
URI permanente para esta colecciónhttps://hdl.handle.net/10953/255
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Examinando DM-Artículos por Materia "Confidence band"
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Ítem Random Linear Operators Arising from Piecewise Linear Interpolation on the Unit Interval(Birkhäuser - Springer, 2022-09-09) Adell, José A.; Cárdenas-Morales, DanielWe introduce a sequence of random linear operators arising from piecewise linear interpolation at a set of random nodes on the unit interval. We show that such operators uniformly converge in probability to the target function, providing at the same time rates of convergence. Analogous results are shown for their deterministic counterparts, derived by taking expectations of the aforementioned random operators. Special attention is paid to the case in which the random nodes are the uniform order statistics, where an explicit form for their associated deterministic operators is provided. This allows us to compare the speed of convergence of the aforementioned operators with that of the random and deterministic Bernstein polynomialsÍtem Stochastic Bernstein polynomials: uniform convergence in probability with rates(Springer, 2020-02-27) Adell, José A.; Cárdenas-Morales, DanielWe introduce stochastic variants of the classical Bernstein polynomials associated with a continuous function f , built up from a general triangular array of random variables. We discuss the uniform convergence in probability of the approximation process that they represent, providing at the same time rates of convergence. In the particular case in which the triangular array of random variables consists of the uniform order statistics, we give a positive answer to a conjectured raised in Wu and Zhou (Adv. Comput. Math. 46, 8, 2020) about an exponential rate of convergence in probability.