B1378
Title: Smooth distribution function estimation for lifetime distributions using Szasz-Mirakyan operators
Authors: Bernhard Klar - Karlsruhe institute of Technology (Germany) [presenting]
Ariane Hanebeck - Technical University of Munich (Germany)
Abstract: A new smooth estimator for continuous distribution functions is introduced on the positive real half-line using Szasz-Mirakyan operators, similar to Bernstein's approximation theorem. The Bernstein basis polynomials, given by binomial probabilities, are replaced by Poisson probabilities. It is shown that the proposed estimator outperforms the empirical distribution function in terms of asymptotic (integrated) mean-squared error and generally compares favourably with other competitors in theoretical comparisons. Proposals for a data-driven choice of bandwidth are discussed. Also, the results of simulations are shown to demonstrate the finite sample performance of the proposed estimator.
