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

@article{Hanebeck2021SmoothDF,
  title={Smooth distribution function estimation for lifetime distributions using Szasz–Mirakyan operators},
  author={Ariane Hanebeck and Bernhard Klar},
  journal={Annals of the Institute of Statistical Mathematics},
  year={2021}
}
In this paper, we introduce a new smooth estimator for continuous distribution functions on the positive real half-line using Szasz-Mirakyan Operators. The approach is similar to the idea of the Bernstein estimator. We show 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 and in a simulation study. 

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