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Nonparametric recursive method for moment generating function kernel-type estimators

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  • Bouzebda, Salim
  • Slaoui, Yousri

Abstract

In the present paper, we are mainly concerned with the kernel type estimators for the moment generating function. More precisely, we establish the central limit theorem together with the characterization of the bias and the variance for the nonparametric recursive kernel-type estimators for the moment generating function under some mild conditions. Finally, we investigate the performance of the methodology for small samples through a short simulation study.

Suggested Citation

  • Bouzebda, Salim & Slaoui, Yousri, 2022. "Nonparametric recursive method for moment generating function kernel-type estimators," Statistics & Probability Letters, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:stapro:v:184:y:2022:i:c:s0167715222000359
    DOI: 10.1016/j.spl.2022.109422
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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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    5. Norbert Henze & Jaco Visagie, 2020. "Testing for normality in any dimension based on a partial differential equation involving the moment generating function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1109-1136, October.
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    7. 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.
    8. Salim Bouzebda & Thouria El-hadjali, 2020. "Uniform convergence rate of the kernel regression estimator adaptive to intrinsic dimension in presence of censored data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 32(4), pages 864-914, October.
    9. Salim Bouzebda & Issam Elhattab & Boutheina Nemouchi, 2021. "On the uniform-in-bandwidth consistency of the general conditional U-statistics based on the copula representation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 33(2), pages 321-358, April.
    10. Salim Bouzebda & Boutheina Nemouchi, 2020. "Uniform consistency and uniform in bandwidth consistency for nonparametric regression estimates and conditional U-statistics involving functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 32(2), pages 452-509, April.
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