ON THE USE OF THE EMPIRICAL DISTRIBUTION AND CHARACTERISTIC FUNCTION TO ESTIMATE PARAMETERS OF REGULAR VARIATION

In this paper we present two new classes of estimators of parameters of regular variation, one based on the empirical distribution function and the other on the empirical characteristic function. They achieve the same rates of mean square error convergence as the estimators proposed by Hall (1982). The estimator based on the empirical characteristic function, unlike the other estimators, utilises the whole sample and not just a few extreme order statistics.