The integrated squared error estimation of parameters

Abstract

SUMMARY The paper develops in a more general setting the methods used by Paulson, Holcomb & Leitoh (1976) to estimate the parameters of a stable law. The statistic considered minimizes a distance function determined by the empirical characteristic function. Consistency is established under the condition of differentiability of the characteristic function and the existence of bounded second derivatives is required to obtain a central limit theorem for the estimators of one or more parameters. Questions concerning efficiency and robustness are discussed.