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Minimum distance estimation in normed linear spaces with Donsker-classes

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Abstract

We consider minimum distance estimators where the discrepancy function is defined in terms of a supremum-norm based on a Donsker-class of functions. If the parameter set is contained in a normed linear space we prove a Portmanteau-type theorem. Here, the limit in general is not a probability measure, but an outer measure given by the hitting family of the set of all minimizing points of a certain stochastic process. In case there is exactly one minimizer one obtains traditional weak convergence.

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Authors and Affiliations

  1. Dept. of Math., Techn. Univ., Dresden, Germany

    D. Ferger

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  1. D. Ferger
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Correspondence to D. Ferger.

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Ferger, D. Minimum distance estimation in normed linear spaces with Donsker-classes. Math. Meth. Stat. 19, 246–266 (2010). https://doi.org/10.3103/S1066530710030038

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  • DOI: https://doi.org/10.3103/S1066530710030038

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