Abstract
The semi-parametric transformation models under length-biased sampling are considered. The well-known proportional hazards model and proportional odds model are special cases of the semi-parametric transformation models. Empirical likelihood and adjusted empirical likelihood inferences for semi-parametric transformation models with length-biased sampling are proposed, and the empirical log-likelihood ratio test statistic is shown to converge to a standard chi-squared distribution. In addition, statistical inferences for the regression parameters are made based on the results. Moreover, extensive simulation studies are carried out. Finally, a real data set is analyzed to illustrate the proposed empirical likelihood and adjusted empirical likelihood methods.
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