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Generalised gamma kernel density estimation for nonnegative data and its bias reduction

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  • Gaku Igarashi
  • Yoshihide Kakizawa

Abstract

We consider density estimation for nonnegative data using generalised gamma density. What is being emphasised here is that a negative exponent is allowed. We show that, for each positive or negative exponent, (i) generalised gamma kernel density estimator, without bias reduction, has the mean integrated squared error (MISE) of order $ O(n^{-4/5}) $ O(n−4/5), as in other boundary-bias-free density estimators from the existing literature, and that (ii) the bias-reduced versions have the MISEs of order $ O(n^{-8/9}) $ O(n−8/9), where n is the sample size. We illustrate the finite sample performance of the proposed estimators through the simulations.

Suggested Citation

  • Gaku Igarashi & Yoshihide Kakizawa, 2018. "Generalised gamma kernel density estimation for nonnegative data and its bias reduction," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(3), pages 598-639, July.
    • Handle: RePEc:taf:gnstxx:v:30:y:2018:i:3:p:598-639
    DOI: 10.1080/10485252.2018.1457791
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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. 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.
    3. Kakizawa, Yoshihide, 2021. "A class of Birnbaum–Saunders type kernel density estimators for nonnegative data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    4. Pierre Lafaye de Micheaux & Frédéric Ouimet, 2021. "A Study of Seven Asymmetric Kernels for the Estimation of Cumulative Distribution Functions," Mathematics, MDPI, vol. 9(20), pages 1-35, October.
    5. 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).
    6. 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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