Smooth distribution function estimation for lifetime distributions using Szasz–Mirakyan operators

Ariane Hanebeck () and Bernhard Klar ()
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Ariane Hanebeck: Technical University of Munich
Bernhard Klar: Karlsruhe Institute of Technology

Annals of the Institute of Statistical Mathematics, 2021, vol. 73, issue 6, No 7, 1229-1247

Abstract: Abstract In this paper, 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. 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. Also, we conduct the simulations to demonstrate the finite sample performance of the proposed estimator.

Keywords: Distribution function estimation; Nonparametric; Szasz–Mirakyan operator; Hermite estimator; Mean squared error (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10463-020-00783-y

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