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Family of the generalised gamma kernels: a generator of asymmetric kernels for nonnegative data

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  • Masayuki Hirukawa
  • Mari Sakudo

Abstract

Unlike symmetric kernels, so far exploring asymptotics on asymmetric kernels has relied on diversified approaches. This paper proposes a family of the generalised gamma (GG) kernels that is built on the probability density function of the GG distribution [Stacy, E.W. (1962), 'A Generalization of the Gamma Distribution', Annals of Mathematical Statistics , 33, 1187-1192] and a few common conditions. The family can generate asymmetric kernels that share appealing properties with the modified gamma kernel [Chen, S.X. (2000), 'Probability Density Function Estimation Using Gamma Kernels', Annals of the Institute of Statistical Mathematics , 52, 471-480]. Asymptotics on the kernels generated from the family can be delivered by manipulating the conditions directly, as with symmetric kernels.

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  • Masayuki Hirukawa & Mari Sakudo, 2015. "Family of the generalised gamma kernels: a generator of asymmetric kernels for nonnegative data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 41-63, March.
    • Handle: RePEc:taf:gnstxx:v:27:y:2015:i:1:p:41-63
    DOI: 10.1080/10485252.2014.998669
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    2. Hagmann, M. & Scaillet, O., 2007. "Local multiplicative bias correction for asymmetric kernel density estimators," Journal of Econometrics, Elsevier, vol. 141(1), pages 213-249, November.
    3. Olivier SCAILLET, 2001. "Density Estimation Using Inverse and Reciprocal Inverse Guassian Kernels," LIDAM Discussion Papers IRES 2001017, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    4. 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.
    5. Bouezmarni, Taoufik & Rombouts, Jeroen V.K., 2010. "Nonparametric density estimation for positive time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 245-261, February.
    6. Malec, Peter & Schienle, Melanie, 2014. "Nonparametric kernel density estimation near the boundary," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 57-76.
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    9. 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.
    10. Hirukawa, Masayuki & Sakudo, Mari, 2014. "Nonnegative bias reduction methods for density estimation using asymmetric kernels," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 112-123.
    11. Gospodinov, Nikolay & Hirukawa, Masayuki, 2012. "Nonparametric estimation of scalar diffusion models of interest rates using asymmetric kernels," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 595-609.
    12. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
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    4. Kakizawa, Yoshihide, 2021. "A class of Birnbaum–Saunders type kernel density estimators for nonnegative data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
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    6. Masayuki Hirukawa & Mari Sakudo, 2016. "Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels," Econometrics, MDPI, vol. 4(2), pages 1-27, June.
    7. 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.
    8. 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.
    9. Hirukawa, Masayuki & Sakudo, Mari, 2019. "Another bias correction for asymmetric kernel density estimation with a parametric start," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 158-165.
    10. Funke, Benedikt & Hirukawa, Masayuki, 2019. "Nonparametric estimation and testing on discontinuity of positive supported densities: a kernel truncation approach," Econometrics and Statistics, Elsevier, vol. 9(C), pages 156-170.
    11. Funke, Benedikt & Hirukawa, Masayuki, 2021. "Bias correction for local linear regression estimation using asymmetric kernels via the skewing method," Econometrics and Statistics, Elsevier, vol. 20(C), pages 109-130.
    12. Lynda Harfouche & Smail Adjabi & Nabil Zougab & Benedikt Funke, 2018. "Multiplicative bias correction for discrete kernels," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 253-276, June.
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    14. 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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