The Estimators Of Extreme Value Index With Block Method

This paper mainly established extreme index estimators when only a few largest values are observed within blocks.Suppose {Xnn,n?1} is a sequence of independent and identically distributed random variables.We divide the samples into several blocks,construct estimator by using the samples in each block and then show the asymptotical properties of these estimators.Simulation studies are illustrated to compare the estima-tors with several estimators proposed in the literature.An application of the estimators is to estimate the tail index of Danish data on large fire insurance losses.We construct the Hill type estimator with the block method in section 2,and further prove the weak convergence and asymptotic normality of them under the second order regular variation condition.For ? ? R,we propose a new Pickands type estimator and study its asymptotical properties in section 3.Simulation studies through Monte Calor method are presented in section 4.We discuss the threshold selection question and compare the two type estimators proposed in this paper with the estimators proposed by Qi(2010)[38],Pickands estimator and the DPR estimator under minimum mean squared error criterion.Finally the new estimators were used on Danish data on large fire insurance losses from 1980 to 1990,and analysis shows that the estimates are acceptable.