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New kernel estimators of the hazard ratio and their asymptotic properties

Author

Listed:
  • Taku Moriyama

    (Kyushu University)

  • Yoshihiko Maesono

    (Kyushu University)

Abstract

We propose a kernel estimator of a hazard ratio that is based on a modification of Ćwik and Mielniczuk (Commun Stat-Theory Methods 18(8):3057–3069, 1989)’s method. A naive nonparametric estimator is Watson and Leadbetter (Sankhyā: Indian J Stat Ser A 26(1):101–116, 1964)’s one, which is naturally given by the kernel density estimator and the empirical distribution estimator. We compare the asymptotic mean squared error (AMSE) of the hazard estimators, and then, it is shown that the asymptotic variance of the new estimator is usually smaller than that of the naive one. We also discuss bias reduction of the proposed estimator and derived some modified estimators. While the modified estimators do not lose nonnegativity, their AMSE is small both theoretically and numerically.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:1:d:10.1007_s10463-018-0685-6
    DOI: 10.1007/s10463-018-0685-6
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    References listed on IDEAS

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    1. Vieu, Philippe, 1991. "Quadratic errors for nonparametric estimates under dependence," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 324-347, November.
    2. McCune, E. D. & McCune, S. K., 1987. "On improving convergence rates for nonnegative kernel failure-rate function estimators," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 71-76, November.
    3. 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.
    4. 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.
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