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

Hammou El Barmi and Lahcen El Bermi

Journal of Nonparametric Statistics, 2013, vol. 25, issue 2, 487-498

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.

Date: 2013
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DOI: 10.1080/10485252.2013.772177

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