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Nonparametric density estimation based on beta prime kernel

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  • Elif Erçelik
  • Mustafa Nadar

Abstract

In this work, we propose beta prime kernel estimator for estimation of a probability density functions defined with nonnegative support. For the proposed estimator, beta prime probability density function used as a kernel. It is free of boundary bias and nonnegative with a natural varying shape. We obtained the optimal rate of convergence for the mean squared error (MSE) and the mean integrated squared error (MISE). Also, we use adaptive Bayesian bandwidth selection method with Lindley approximation for heavy tailed distributions and compare its performance with the global least squares cross-validation bandwidth selection method. Simulation studies are performed to evaluate the average integrated squared error (ISE) of the proposed kernel estimator against some asymmetric competitors using Monte Carlo simulations. Moreover, real data sets are presented to illustrate the findings.

Suggested Citation

  • Elif Erçelik & Mustafa Nadar, 2020. "Nonparametric density estimation based on beta prime kernel," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(2), pages 325-342, January.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:2:p:325-342
    DOI: 10.1080/03610926.2018.1538458
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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. Kakizawa, Yoshihide, 2021. "A class of Birnbaum–Saunders type kernel density estimators for nonnegative data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    3. 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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