Invariance principles for von Mises and U-statistics |
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Authors: | Herold Dehling Manfred Denker Walter Philipp |
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Affiliation: | (1) Institut für Mathematische Stochastik, Universität Göttingen, Lotzestr. 13, D-3400 Göttingen, Germany;(2) Department of Mathematics, University of Illinois, 1409 West Green Street, 61801 Urbana, IL, USA |
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Abstract: | Summary The almost sure approximation of von Mises-statistics and U-statistics by appropriate stochastic integrals with respect to Kiefer processes is obtained. In general these integrals are non-Gaussian processes. As applications we get almost sure versions for the estimator of the variance and for the 2-test of goodness of fit.This work was done while the last author was a visiting professor at the Institut für Mathematische Stochastik at the University of Göttingen during the Spring of 1982. He thanks the Institut and its members for their hospitality |
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