Conditional quantile estimation with auxiliary information for left-truncated and dependent data

In this paper, the empirical likelihood method is used to define a new estimator of conditional quantile in the presence of auxiliary information for the left-truncation model. The asymptotic normality of the estimator is established when the data exhibit some kind of dependence. It is assumed that the lifetime observations with multivariate covariates form a stationary α ‐ mixing sequence. The result shows that the asymptotic variance of the proposed estimator is not larger than that of standard kernel estimator. Finite sample behavior of the estimator is investigated via simulations too.