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

Author

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  • Ariane Hanebeck

    (Technical University of Munich)

  • Bernhard Klar

    (Karlsruhe Institute of Technology)

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.

Suggested Citation

  • Ariane Hanebeck & Bernhard Klar, 2021. "Smooth distribution function estimation for lifetime distributions using Szasz–Mirakyan operators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1229-1247, December.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:6:d:10.1007_s10463-020-00783-y
    DOI: 10.1007/s10463-020-00783-y
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    References listed on IDEAS

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    1. Yousri Slaoui, 2014. "Bandwidth Selection for Recursive Kernel Density Estimators Defined by Stochastic Approximation Method," Journal of Probability and Statistics, Hindawi, vol. 2014, pages 1-11, June.
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    3. Choongrak Kim & Sungsoo Kim & Mira Park & Hakbae Lee, 2006. "A bias reducing technique in kernel distribution function estimation," Computational Statistics, Springer, vol. 21(3), pages 589-601, December.
    4. M. Falk, 1983. "Relative efficiency and deficiency of kernel type estimators of smooth distribution functions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 37(2), pages 73-83, June.
    5. Asma Jmaei & Yousri Slaoui & Wassima Dellagi, 2017. "Recursive distribution estimator defined by stochastic approximation method using Bernstein polynomials," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 792-805, October.
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    Cited by:

    1. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    2. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    3. Pierre Lafaye de Micheaux & Frédéric Ouimet, 2021. "A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions," Mathematics, MDPI, vol. 9(20), pages 1-35, October.

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