Abstract
The theorem of the iterated logarithm for one-dimensional empirical distribution functions (DF)-as given in [4]-is generalized to the case of ℝk;k>1. As examples of application the exact value of the barrier in a well-known lemma of Smirnov-Chung-Kiefer for general DF and a sharpened version of the Glivenko-Cantelli theorem in ℝk are derived.
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Literatur
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Richter, H. Das Gesetz vom iterierten Logarithmus für empirische Verteilungsfunktionen im ℝk . Manuscripta Math 11, 291–303 (1974). https://doi.org/10.1007/BF01173720
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DOI: https://doi.org/10.1007/BF01173720