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Empirical likelihood ratio test for symmetry against type I bias with applications to competing risks

Author

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  • Hammou El Barmi
  • Lahcen El Bermi

Abstract

A random variable X with cumulative distribution function F is said to have a symmetric distribution about θ if and only if X - θ and - X +θ are identically distributed. Different types of partial skewness and one-sided bias are obtained by looking at different types of orderings between the distributions of X - θ and - X +θ. For example, X , or equivalently F , is said to have type I bias about θ if X - θ is stochastically larger than - X +θ. In this paper, we assume that F is continuous, θ is known and develops an empirical likelihood ratio type test for testing for symmetry about θ against this type of alternative. This test is shown to be asymptotically distribution free and the results of a simulation study show that it outperforms in terms of power, a test developed for the same problem in Alfieri and El Barmi [(2005), 'Nonparametric Estimation of a Distribution Function with Type I Bias with Applications to Competing Risks', Journal of Nonparametric Statistics , 17, 319-333]. It turns out that the results developed here can be extended in a natural way to compare the sub-survival functions corresponding to two risks in a competing risks setting. We show how this can be done and illustrate our theoretical results with a real life example.

Suggested Citation

  • Hammou El Barmi & Lahcen El Bermi, 2013. "Empirical likelihood ratio test for symmetry against type I bias with applications to competing risks," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 487-498, June.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:487-498
    DOI: 10.1080/10485252.2013.772177
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    References listed on IDEAS

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    1. Einmahl, J.H.J. & McKeague, I.W., 2002. "Empirical Likelihood based on Hypothesis Testing," Other publications TiSEM 402576fa-8c0e-45e2-a394-8, Tilburg University, School of Economics and Management.
    2. Richard Dykstra & Subhash Kochar & Tim Robertson, 1995. "Likelihood ratio tests for symmetry against one-sided alternatives," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 719-730, December.
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