Some characterizations of almost sure bounds for weighted multidimensional empirical distributions and a Glivenko-Cantelli theorem for sample quantiles

SummaryCharacterizations of almost sure bounds and a Glivenko-Cantelli theorem are obtained for certain weighted m-dimensional empirical distributions. These results constitute generalizations and extensions of the work of Shorack and Wellner (1978) and Wellner (1977, 1978). Also as an example of the potential use of the techniques developed in this paper a Glivenko-Cantelli type theorem is proven for sample quantiles.

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