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Body tail adaptive kernel density estimation for nonnegative heavy-tailed data

Author

Listed:
  • Ziane Yasmina

    (Research Unit LaMOS, Faculty of Exact Sciences, Bejaia University, 06000Bejaia, Algeria)

  • Zougab Nabil

    (Research Unit LaMOS, Faculty of Exact Sciences, Bejaia University, 06000Bejaia, Algeria)

  • Adjabi Smail

    (Research Unit LaMOS, Faculty of Exact Sciences, Bejaia University, 06000Bejaia, Algeria)

Abstract

In this paper, we consider the procedure for deriving variable bandwidth in univariate kernel density estimation for nonnegative heavy-tailed (HT) data. These procedures consider the Birnbaum–Saunders power-exponential (BS-PE) kernel estimator and the bayesian approach that treats the adaptive bandwidths. We adapt an algorithm that subdivides the HT data set into two regions, high density region (HDR) and low-density region (LDR), and we assign a bandwidth parameter for each region. They are derived by using a Monte Carlo Markov chain (MCMC) sampling algorithm. A series of simulation studies and real data are realized for evaluating the performance of a procedure proposed.

Suggested Citation

  • Ziane Yasmina & Zougab Nabil & Adjabi Smail, 2021. "Body tail adaptive kernel density estimation for nonnegative heavy-tailed data," Monte Carlo Methods and Applications, De Gruyter, vol. 27(1), pages 57-69, March.
    • Handle: RePEc:bpj:mcmeap:v:27:y:2021:i:1:p:57-69:n:3
    DOI: 10.1515/mcma-2021-2082
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    References listed on IDEAS

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    1. Y. Ziane & S. Adjabi & N. Zougab, 2015. "Adaptive Bayesian bandwidth selection in asymmetric kernel density estimation for nonnegative heavy-tailed data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(8), pages 1645-1658, August.
    2. Zougab, Nabil & Adjabi, Smail & Kokonendji, Célestin C., 2014. "Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 28-38.
    3. N. Zougab & S. Adjabi & C. Kokonendji, 2012. "Binomial kernel and Bayes local bandwidth in discrete function estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 783-795.
    4. Yasmina Ziane & Nabil Zougab & Smail Adjabi, 2018. "Birnbaum–Saunders power-exponential kernel density estimation and Bayes local bandwidth selection for nonnegative heavy tailed data," Computational Statistics, Springer, vol. 33(1), pages 299-318, March.
    5. Hu, Shuowen & Poskitt, D.S. & Zhang, Xibin, 2012. "Bayesian adaptive bandwidth kernel density estimation of irregular multivariate distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 732-740.
    6. Marchant, Carolina & Bertin, Karine & Leiva, Víctor & Saulo, Helton, 2013. "Generalized Birnbaum–Saunders kernel density estimators and an analysis of financial data," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 1-15.
    7. Kundu, Debasis & Kannan, Nandini & Balakrishnan, N., 2008. "On the hazard function of Birnbaum-Saunders distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2692-2702, January.
    8. Xiaodong Jin & Janusz Kawczak, 2003. "Birnbaum-Saunders and Lognormal Kernel Estimators for Modelling Durations in High Frequency Financial Data," Annals of Economics and Finance, Society for AEF, vol. 4(1), pages 103-124, May.
    Full references (including those not matched with items on IDEAS)

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