Seminar of the Department of Probability and Statistics

On Tuesday, October 10, 2023 at 4:15 p.m., in room 840, a lecture will be held: prof. Dr. Bernard Klar (Institute of Stochastics, Karlsruhe Institute of Technology)

SMOOTH DISTRIBUTION FUNCTION ESTIMATION FOR LIFETIME DISTRIBUTIONS USING SZASZ-MIRAKYAN OPERATORS

Summary: 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 Bernstein's 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.

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Meeting ID: 990 5244 7752 Passcode: 713997