Estimating a Stability Parameter: Asymptotics and Simulations

Abstract

Observing the nin absolute value largest out of t symmetric stable i.i.d. random variables, we compare different estimators for the stability parameter α ∈ (0,2). We determine two asymptotically efficient estimator sequences for α, and consider also the Hill estimator. Interesting differences arise when finite sample size performance is investigated by simulations.

AMS Subject Classification::

• 60G55
• 62F12
• 62F11

Keywords:

• Stable laws
• Poisson point processes
• parameter estimation
• asymptotic efficiency
• finite sample size properties