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Limiting bias-reduced Amoroso kernel density estimators for non-negative data

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  • Gaku Igarashi
  • Yoshihide Kakizawa

Abstract

The Amoroso kernel density estimator (Igarashi and Kakizawa 2017) for non-negative data is boundary-bias-free and has the mean integrated squared error (MISE) of order O(n− 4/5), where n is the sample size. In this paper, we construct a linear combination of the Amoroso kernel density estimator and its derivative with respect to the smoothing parameter. Also, we propose a related multiplicative estimator. We show that the MISEs of these bias-reduced estimators achieve the convergence rates n− 8/9, if the underlying density is four times continuously differentiable. We illustrate the finite sample performance of the proposed estimators, through the simulations.

Suggested Citation

  • Gaku Igarashi & Yoshihide Kakizawa, 2018. "Limiting bias-reduced Amoroso kernel density estimators for non-negative data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(20), pages 4905-4937, October.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:20:p:4905-4937
    DOI: 10.1080/03610926.2017.1380832
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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. Kakizawa, Yoshihide, 2021. "A class of Birnbaum–Saunders type kernel density estimators for nonnegative data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).

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