Семинар Катедре за вероватноћу и статистику, 10. октобар 2023.

• 04. Октобар, 2023
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Наредни састанак Семинара биће одржан у уторак, 10. октобра 2023. у сали 840 Математичког факултета (Студентски трг 16, В спрат) са почетком у 16.15.

Предавач: prof. dr Bernhard Klar, Karlsruhe Institute of Technology (KIT) Institute of Stochastics
 
Наслов предавања: SMOOTH DISTRIBUTION FUNCTION ESTIMATION FOR LIFETIME DISTRIBUTIONS USING SZASZ-MIRAKYAN OPERATORS
 
Апстракт: In this talk, we introduce a new smooth estimator for continuous distribution functions on the positive real half-line using Szasz-Mirakyan operators, similar to Bernsteins approximation theorem. Here, the Bernstein basis polynomials, given by binomial probabilities, are replaced by Poisson probabilities. We show that the proposed estimator outperforms the empirical distribution function in terms of asymptotic (integrated) mean-squared error, and  generally compares favorably with other competitors in theoretical comparisons. We discuss proposals for a data-driven choice of bandwidth. Also, we show the results of simulations to demonstrate the finite sample performance of the proposed estimator.