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Nonnegative bias reduction methods for density estimation using asymmetric kernels

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  • Hirukawa, Masayuki
  • Sakudo, Mari

Abstract

Two classes of multiplicative bias correction (“MBC”) methods are applied to density estimation with support on [0,∞). It is demonstrated that under sufficient smoothness of the true density, each MBC technique reduces the order of magnitude in bias, whereas the order of magnitude in variance remains unchanged. Accordingly, the mean integrated squared error of each MBC estimator achieves a faster convergence rate of O(n−8/9) when best implemented, where n is the sample size. Furthermore, MBC estimators always generate nonnegative estimates by construction. Plug-in smoothing parameter choice rules for the estimators are proposed, and their finite sample performance is examined via Monte Carlo simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:75:y:2014:i:c:p:112-123
    DOI: 10.1016/j.csda.2014.01.012
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Gustafsson, J. & Hagmann, M. & Nielsen, J. P. & Scaillet, O., 2009. "Local Transformation Kernel Density Estimation of Loss Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 161-175.
    4. McKinley Blackburn & David Neumark, 1992. "Unobserved Ability, Efficiency Wages, and Interindustry Wage Differentials," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(4), pages 1421-1436.
    5. David Romer, 1993. "Openness and Inflation: Theory and Evidence," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(4), pages 869-903.
    6. 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.
    7. 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.
    8. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    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.
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    Cited by:

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    3. Kanaya, S. & Bhattacharya, D., 2017. "Uniform Convergence of Smoothed Distribution Functions with an Application to Delta Method for the Lorenz Curve," Cambridge Working Papers in Economics 1760, Faculty of Economics, University of Cambridge.
    4. 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.
    5. 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.
    6. 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.
    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. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    9. 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.
    10. M. Hiabu & E. Mammen & M. D. Martìnez-Miranda & J. P. Nielsen, 2016. "In-sample forecasting with local linear survival densities," Biometrika, Biometrika Trust, vol. 103(4), pages 843-859.
    11. 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.
    12. Gaku Igarashi, 2016. "Bias reductions for beta kernel estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 1-30, March.
    13. Mohammadi, Faezeh & Izadi, Muhyiddin & Lai, Chin-Diew, 2016. "On testing whether burn-in is required under the long-run average cost," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 217-224.
    14. Gery Geenens, 2021. "Mellin–Meijer kernel density estimation on $${{\mathbb {R}}}^+$$ R +," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 953-977, October.
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    16. 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.

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