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Smoothed Empirical Likelihood Testing for Quantile Regression Models under Right Censorship

This paper is focused on testing the parameters of the quantile regression models. For complete observation, it is shown in literature that the test statistics, based on empirical likelihood (EL) method and smoothed empirical likelihood (SEL) method, both converge weakly to the standard Chi-square distribution $\chi_M^2$ under the null hypothesis. For right censored data, the statistics in literature, by the EL method, have a weighted Chi-square limiting distribution, but the weights are unknown. In this paper, we show that the statistics based on the EL method and the SEL method also converge weakly to $\chi_M^2$ under the null hypothesis, so there is no need to estimate any weights. As its estimating function is smoothed, the SEL method can be Bartlett corrected. Numerical results show that the SEL method, via Bartlett correction, outperforms some recent methods.