Kernel-type estimator of the conditional tail expectation for a heavy-tailed distribution

Abstract

In this paper, we are interested in the generalization and improvement of the estimator of the conditional tail expectation (CTE) for a heavy-tailed distribution when the second moment is infinite. It is well known that classical estimators of the CTE are seriously biased under the second-order regular variation framework. To reduce the bias, many authors proposed the use of so-called second-order reduced bias estimators for both first-order and second-order tail parameters. In this work, we have generalized a kernel-type estimator, and we present a number of results on its distributional behavior and compare its performance with the performance of other estimators.