Semiparametric tail-index estimation for randomly right-truncated heavy-tailed data

It was shown that when one disposes of a parametric information of the truncation distribution, the semiparametric estimator of the distribution function for truncated data (Wang, 1989) is more efficient than the nonparametric one. On the basis of this estimation method, we derive an estimator for the tail index of Pareto-type distributions that are randomly right-truncated and establish its consistency and asymptotic normality. The finite sample behavior of the proposed estimator is carried out by simulation study. We point out that, in terms of both bias and root of the mean squared error, our estimator performs better than those based on nonparametric estimation methods. An application to a real dataset of induction times of AIDS diseases is given as well.