Tail empirical process and a weighted extreme value index estimator for randomly right-censored data
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A tail empirical process for heavy-tailed and right-censored data is introduced and its Gaussian approximation is established. In this context, a (weighted) new Hill-type estimator for positive extreme value index is proposed and its consistency and asymptotic normality are proved by means of the aforementioned process and the second-order conditions of regular variation framework. Our approach may also be served to develop other statistics related to the distribution tail as second-order parameter estimators and reduced-bias tail index estimators as well as their consistency and asymptotic normality. Moreover, the proposed tail empirical process provide a goodness of fit test for Pareto-like models under censorship. In a comparative simulation study, the newly defined estimator is seen to perform better than the already existing ones in terms of both bias and mean squared error. Finally, an application to the survival time of Australian male Aids patients is provided.
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