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Re-formulation of inverse Gaussian, reciprocal inverse Gaussian, and Birnbaum–Saunders kernel estimators

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  • Igarashi, Gaku
  • Kakizawa, Yoshihide

Abstract

We reveal the boundary bias problem of Birnbaum–Saunders, inverse Gaussian, and reciprocal inverse Gaussian kernel estimators (Jin and Kawczak, 2003; Scaillet, 2004) and re-formulate these estimators to solve the problem. We investigate asymptotic properties of a new class of asymmetric kernel estimators.

Suggested Citation

  • Igarashi, Gaku & Kakizawa, Yoshihide, 2014. "Re-formulation of inverse Gaussian, reciprocal inverse Gaussian, and Birnbaum–Saunders kernel estimators," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 235-246.
    • Handle: RePEc:eee:stapro:v:84:y:2014:i:c:p:235-246
    DOI: 10.1016/j.spl.2013.10.013
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    References listed on IDEAS

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    1. Alexandre Leblanc, 2010. "A bias-reduced approach to density estimation using Bernstein polynomials," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 459-475.
    2. Gaku Igarashi & Yoshihide Kakizawa, 2014. "On improving convergence rate of Bernstein polynomial density estimator," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 61-84, March.
    3. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 471-480, September.
    4. M.C. Jones & D.A. Henderson, 2007. "Miscellanea Kernel-Type Density Estimation on the Unit Interval," Biometrika, Biometrika Trust, vol. 94(4), pages 977-984.
    5. 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.
    6. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    7. Hirukawa, Masayuki, 2010. "Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 473-495, February.
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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. Xu Li & Juxia Xiao & Weixing Song & Jianhong Shi, 2019. "Local linear regression with reciprocal inverse Gaussian kernel," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 733-758, August.
    4. Kakizawa, Yoshihide, 2022. "Multivariate elliptical-based Birnbaum–Saunders kernel density estimation for nonnegative data," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    5. 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.
    6. 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.
    7. Gaku Igarashi, 2016. "Bias reductions for beta kernel estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 1-30, March.

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