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Multivariate generalized Birnbaum—Saunders kernel density estimators

Author

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  • N. Zougab
  • L. Harfouche
  • Y. Ziane
  • S. Adjabi

Abstract

In this article, we first propose the classical multivariate generalized Birnbaum–Saunders kernel estimator for probability density function estimation in the context of multivariate non negative data. Then, we apply two multiplicative bias correction (MBC) techniques for multivariate kernel density estimator. Some properties (bias, variance, and mean integrated squared error) of the corresponding estimators are also investigated. Finally, the performances of the classical and MBC estimators based on family of generalized Birnbaum–Saunders kernels are illustrated by a simulation study.

Suggested Citation

  • N. Zougab & L. Harfouche & Y. Ziane & S. Adjabi, 2018. "Multivariate generalized Birnbaum—Saunders kernel density estimators," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(18), pages 4534-4555, September.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:18:p:4534-4555
    DOI: 10.1080/03610926.2017.1377252
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    Cited by:

    1. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    2. 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.
    3. Célestin C. Kokonendji & Sobom M. Somé, 2021. "Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics," Stats, MDPI, vol. 4(1), pages 1-22, March.
    4. Kakizawa, Yoshihide, 2022. "Multivariate elliptical-based Birnbaum–Saunders kernel density estimation for nonnegative data," Journal of Multivariate Analysis, Elsevier, vol. 187(C).

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