ESTIMATING A STABILITY PARAMETER - ASYMPTOTICS AND SIMULATIONS

Observing the n in absolute value largest out of a symmetric stable i. i.d. random variables, we compare different estimators for the stabili ty parameter alpha is an element of (0,2). We determine two asymptotic ally efficient estimator sequences for alpha, and consider also the Hi ll estimator. Interesting differences arise when finite sample size pe rformance is investigated by simulations.