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Nonparametric density estimation for multivariate bounded data using two non-negative multiplicative bias correction methods

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  • Funke, Benedikt
  • Kawka, Rafael

Abstract

Two new multiplicative bias correction techniques for nonparametric multivariate density estimation in the context of positively supported data are proposed. Both methods reach an optimal rate of convergence of the mean squared error of order O(n−8/(8+d)), where d is the dimension of the underlying data set. In addition, they overcome the boundary effect and their values are always non-negative. Asymptotic properties like bias and variance are investigated. Moreover, the performance of both estimators is studied in Monte Carlo simulations and in two real data examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:92:y:2015:i:c:p:148-162
    DOI: 10.1016/j.csda.2015.07.006
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    1. 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.
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    7. 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.
    8. Karine Bertin & Nicolas Klutchnikoff, 2014. "Adaptive Estimation of a Density Function using Beta Kernels," Working Papers 2014-08, Center for Research in Economics and Statistics.
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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. Diaa Al Mohamad, 2018. "Towards a better understanding of the dual representation of phi divergences," Statistical Papers, Springer, vol. 59(3), pages 1205-1253, September.
    3. Benedikt Funke & Masayuki Hirukawa, 2025. "On uniform consistency of nonparametric estimators smoothed by the gamma kernel," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(3), pages 459-489, June.
    4. 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.
    5. 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.
    6. Sobom M. Somé & Célestin C. Kokonendji & Smail Adjabi & Naushad A. Mamode Khan & Said Beddek, 2024. "Multiple combined gamma kernel estimations for nonnegative data with Bayesian adaptive bandwidths," Computational Statistics, Springer, vol. 39(2), pages 905-937, April.
    7. 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.
    8. 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.
    9. Taku Moriyama & Yoshihiko Maesono, 2020. "New kernel estimators of the hazard ratio and their asymptotic properties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 187-211, February.
    10. Masayuki Hirukawa & Irina Murtazashvili & Artem Prokhorov, 2022. "Uniform convergence rates for nonparametric estimators smoothed by the beta kernel," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1353-1382, September.
    11. 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.
    12. Ouimet, Frédéric, 2022. "A symmetric matrix-variate normal local approximation for the Wishart distribution and some applications," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    13. 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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