Joint robust parameter estimation for symmetric stable distributions

摘要

Inthis paper we present a robust parameter estimation method for jointlyestimating shape parameter α, scale parameter γ and location parameterδ of a symmetric stable distribution. The proposed estimation methodis based on Probability Integral Transformation (PIT) and robustM-estimators. The procedure is ready to use as besides the theoretical descriptionwe provide the numerical algorithm and all constants andapproximations of functions necessary to compute the estimators. Robustcharacteristics and the asymptotic behaviour of estimator α is investigated.A simulation sequence was carried out to examine statistical propertiesof the estimator α. We perform an application for a data setof returns of some assets listed in Budapest Stock Exchange.