# 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.

## 5 Citations

### On the Le Cam distance between Poisson and Gaussian experiments and the asymptotic properties of Szasz estimators

- MathematicsJournal of Mathematical Analysis and Applications
- 2021

### A local limit theorem for the Poisson distribution and its application to the Le Cam distance between Poisson and Gaussian experiments and asymptotic properties of Szasz estimators

- Mathematics
- 2020

In this paper, we develop a precise local limit theorem for the Poisson distribution. We then apply the result to prove an upper bound on the Le Cam distance between Poisson and Gaussian experiments.…

### A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions

- MathematicsMathematics
- 2021

In this paper, we complement a study recently conducted in a paper of H.A. Mombeni, B. Masouri and M.R. Akhoond by introducing five new asymmetric kernel c.d.f. estimators on the half-line [0,∞),…

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