Estimating a Stability Parameter: Asymptotics and Simulations

摘要

Observing thenin absolute value largest out oftsymmetric stable i.i.d. random variables, we compare different estimators for the stability parameter#x3B1;#x2208;(0,2). We determine two asymptotically efficient estimator sequences for#x3B1;, and consider also the Hill estimator. Interesting differences arise when finite sample size performance is investigated by simulations.