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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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    References listed on IDEAS

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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.
    2. 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.
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    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.
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    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:

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    2. 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.
    3. 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.
    4. 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.
    5. 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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