Empirical likelihood inference for semi-parametric transformation models with length-biased sampling

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. (C) 2018 Elsevier B.V. All rights reserved.