Almost complete convergence of a recursive kernel estimator of the density with complete and censored independent data

Safia Leulmi; Sarra Leulmi; Kenza Assia Mezhoud; Soheir Belaloui

Kybernetika (2025)

  • Issue: 1, page 1-17
  • ISSN: 0023-5954

Abstract

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In this paper, we firstly introduce a recursive kernel estimator of the density in the censored data case. Then, we establish its pointwise and uniform almost complete convergences, with rates, in both complete and censored independent data. Finally, we illustrate the accuracy of the proposed estimators throughout a simulation study.

How to cite

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Leulmi, Safia, et al. "Almost complete convergence of a recursive kernel estimator of the density with complete and censored independent data." Kybernetika (2025): 1-17. <http://eudml.org/doc/299936>.

@article{Leulmi2025,
abstract = {In this paper, we firstly introduce a recursive kernel estimator of the density in the censored data case. Then, we establish its pointwise and uniform almost complete convergences, with rates, in both complete and censored independent data. Finally, we illustrate the accuracy of the proposed estimators throughout a simulation study.},
author = {Leulmi, Safia, Leulmi, Sarra, Mezhoud, Kenza Assia, Belaloui, Soheir},
journal = {Kybernetika},
keywords = {recursive kernel estimator; density; almost complete convergence; censored indepented data; right censored data; rate of convergence},
language = {eng},
number = {1},
pages = {1-17},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Almost complete convergence of a recursive kernel estimator of the density with complete and censored independent data},
url = {http://eudml.org/doc/299936},
year = {2025},
}

TY - JOUR
AU - Leulmi, Safia
AU - Leulmi, Sarra
AU - Mezhoud, Kenza Assia
AU - Belaloui, Soheir
TI - Almost complete convergence of a recursive kernel estimator of the density with complete and censored independent data
JO - Kybernetika
PY - 2025
PB - Institute of Information Theory and Automation AS CR
IS - 1
SP - 1
EP - 17
AB - In this paper, we firstly introduce a recursive kernel estimator of the density in the censored data case. Then, we establish its pointwise and uniform almost complete convergences, with rates, in both complete and censored independent data. Finally, we illustrate the accuracy of the proposed estimators throughout a simulation study.
LA - eng
KW - recursive kernel estimator; density; almost complete convergence; censored indepented data; right censored data; rate of convergence
UR - http://eudml.org/doc/299936
ER -

References

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  1. Amiri, A., Rates of almost sure convergence of families of recursive kernel estimators., Ann. Inst. Stat. Univ. Paris LIV 3 (2010), 3-24. MR2858150
  2. Amiri, A., Machkouri, M. El, , IEEE Trans. 66, Issue: 10 (2020) 6378-6388. MR4173545DOI
  3. Bitouzé, D., Laurent, B., Massart, P., 10.1016/S0246-0203(99)00112-0, Ann. Inst. Henri Poincaré - Probab. Stat. 35 (1999), 735-63. MR1725709DOI10.1016/S0246-0203(99)00112-0
  4. Chen, Y. C., , Biostatist. Epidemiol. 1 (2017), 1, 161-187. DOI
  5. Deheuvels, P., Sur l'estimation séquentielle de la densité., C. R. Acad. Sci. Paris Sér. A 276, (1973), 1119-1121. MR0334393
  6. Devroye, L. P., Wagner, T. J., The strong uniform consistency of kernel density estimates in multivariate analysis - V., North-Holland Publishing Company 1980, pp. 59-77. MR0566330
  7. Guessoum, Z., Ould-Said, E., , Stat. Decisions 26 (2008), 3, 159-177. MR2512266DOI
  8. Kaplan, E. M., Meier, P., , J. Amer. Stat. Assoc. 53 (1958), 282, 457-481. Zbl0089.14801MR0093867DOI
  9. Khardani, S., Semmar, S., , Electron. J. Stat. 8 (2014), 2541-2556. MR3285875DOI
  10. Khardani, S., Slaoui, Y., , ALEA - Latin Amer. J. Probab. Math. Stat. 17 (2020), 389-417. MR4105924DOI
  11. Kitouni, A., Boukeloua, M., Messaci, F., , Stat. Probab. Lett. 96 (2015) , 255-261. MR3281773DOI
  12. Mezhoud, K. A., Mohdeb, Z., Louhichi, S., , J. Korean Stat. Soc. 33 (2014), 1065-1076. MR3233079DOI
  13. Parzen, E., , Ann. Math. Stat. 33 (1962), 1065-1076. Zbl0116.11302MR0143282DOI
  14. Tran, L. T., , IEEE Trans. Inform. Theory 35 (1989), 5, 1103-1108. MR1023252DOI
  15. Wegman, E. J., Davies, H. I., , Ann. Stat. 7 (1979), 2, 316-327. MR0520242DOI
  16. Wolverton, C., Wagner, T. J., , IEEE Trans. 5 (1969), 307-308. DOI
  17. Hoeffding, W., Probability inequalities for sums of bounded random variables., In: The Collected Works of Wassily Hoeffding, Springer 1994, pp. 409-426. MR1307621

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