Heavy tail index estimation based on block order statistics

A new kind of heavy tail index estimator is proposed by using block order statistics in this paper. The weak consistency of the estimator is derived. The asymptotic expansion and asymptotic normality of the estimator are considered under second order regular variation conditions. Small sample simulations are presented in terms of average mean and average mean squared error to support our findings by comparison with two known heavy tail estimators established by block order statistics method.