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Generalized Birnbaum–Saunders kernel density estimators and an analysis of financial data

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  • Marchant, Carolina
  • Bertin, Karine
  • Leiva, Víctor
  • Saulo, Helton

Abstract

The kernel method is a nonparametric procedure used to estimate densities with support in R. When nonnegative data are modeled, the classical kernel density estimator presents a bias problem in the neighborhood of zero. Several methods have been developed to reduce this bias, which include the boundary kernel, data transformation and reflection methods. An alternative proposal is to use kernel estimators based on distributions with nonnegative support, as is the case of the Birnbaum–Saunders (BS), gamma, inverse Gaussian and lognormal models. Generalized BS (GBS) distributions have received considerable attention, due to their properties and their flexibility in modeling different types of data. In this paper, we propose, characterize and implement the kernel method based on GBS distributions to estimate densities with nonnegative support. In addition, we provide a simple method to choose the corresponding bandwidth. In order to evaluate the performance of these new estimators, we conduct a Monte Carlo simulation study. The obtained results are illustrated by analyzing financial real data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:63:y:2013:i:c:p:1-15
    DOI: 10.1016/j.csda.2013.01.013
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    3. Gery Geenens, 2021. "Mellin–Meijer kernel density estimation on $${{\mathbb {R}}}^+$$ R +," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 953-977, October.
    4. Danúbia R. Cunha & Roberto Vila & Helton Saulo & Rodrigo N. Fernandez, 2020. "A General Family of Autoregressive Conditional Duration Models Applied to High-Frequency Financial Data," JRFM, MDPI, vol. 13(3), pages 1-20, March.
    5. Gaku Igarashi, 2018. "Multivariate Density Estimation Using a Multivariate Weighted Log-Normal Kernel," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 247-266, August.
    6. 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.
    7. 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.
    8. Funke, Benedikt & Kawka, Rafael, 2015. "Nonparametric density estimation for multivariate bounded data using two non-negative multiplicative bias correction methods," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 148-162.
    9. V�ctor Leiva & Carolina Marchant & Helton Saulo & Muhammad Aslam & Fernando Rojas, 2014. "Capability indices for Birnbaum-Saunders processes applied to electronic and food industries," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 1881-1902, September.
    10. Kakizawa, Yoshihide, 2022. "Multivariate elliptical-based Birnbaum–Saunders kernel density estimation for nonnegative data," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    11. Kakizawa, Yoshihide, 2021. "A class of Birnbaum–Saunders type kernel density estimators for nonnegative data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    12. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    13. 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.
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