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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.

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  • 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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    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.
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    6. 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.
    7. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    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.
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    14. 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.
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