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Convergence in distribution of minimum-distance estimators

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Abstract

It is shown that (under some regularity conditions) minimum distance estimators for a (possibly multidimensional) real parameter of a family of univariate continuous distribution functions have an asymptotic distribution. If the distance is derived from the mean-square norm it is proved that the asymptotic distribution is normal. Weak convergence of empirical distribution to the Brownian bridge is the essential tool for the proof.

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  1. Fachgruppe Statistik, Universität Konstanz, Postfach 7733, 7750, Konstanz

    E. Bolthausen

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  1. E. Bolthausen
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Bolthausen, E. Convergence in distribution of minimum-distance estimators. Metrika 24, 215–227 (1977). https://doi.org/10.1007/BF01893411

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  • DOI: https://doi.org/10.1007/BF01893411

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