Asymptotically efficient estimation of location for a symmetric stable law. (English) Zbl 0349.62023

Summary: A well-known characteristic function representation of the family of symmetric stable distributions \(\mathcal{F}\) indexes them with a location, scale, and type parameter. A sample of size \(n\) is taken from an unknown member of \(\mathcal{F}\). In this paper, an estimator of the location parameter is constructed which is maximum probability. This means that the estimator conventionally normalized converges in distribution to a normal distribution with zero mean and variance the inverse of the Fisher Information.


62F10 Point estimation
62F12 Asymptotic properties of parametric estimators
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