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Weak and universal consistency of moving weighted averages

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Abstract

The properties of weighted averages as linear estimators of a regression function and its derivatives are investigated for the fixed design case. Results on weak consistency and on universal consistency are derived, using a modification of the definition of Stone [10]. As examples we consider kernel estimates and weighted local regression estimators and show that the general results apply.

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  1. Institut für Medizinisch-Biologische Statistik, Universität Marburg, Ernst-Giller-Strasse 20, D-3550, Marburg, Federal Republic of Germany

    H. -G. Müller

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  1. H. -G. Müller
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Müller, H.G. Weak and universal consistency of moving weighted averages. Period Math Hung 18, 241–250 (1987). https://doi.org/10.1007/BF01848087

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  • DOI: https://doi.org/10.1007/BF01848087

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