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Multivariate Density Estimation Using a Multivariate Weighted Log-Normal Kernel

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  • Gaku Igarashi

    (University of Tsukuba)

Abstract

This paper suggests a multivariate asymmetric kernel density estimation using a multivariate weighted log-normal (LN) kernel for non-negative multivariate data. Asymptotic properties of the multivariate weighted LN kernel density estimator are studied. Simulation studies are also conducted in the bivariate situation.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankha:v:80:y:2018:i:2:d:10.1007_s13171-018-0125-y
    DOI: 10.1007/s13171-018-0125-y
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen VK, 2010. "Nonparametric density estimation for multivariate bounded data," LIDAM Reprints CORE 2301, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. 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.
    6. Gaku Igarashi, 2016. "Weighted log-normal kernel density estimation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(22), pages 6670-6687, November.
    7. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    8. 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.
    9. Hira L. Koul & Weixing Song, 2013. "Large sample results for varying kernel regression estimates," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 829-853, December.
    10. Mnatsakanov, Robert & Sarkisian, Khachatur, 2012. "Varying kernel density estimation on R+," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1337-1345.
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    Cited by:

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    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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