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Asymptotics of Studentized |
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| Authors: | M. Csörgõ B. Szyszkowicz Q. Wang |
| Affiliation: | (1) School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON, Canada, K1S 5B6;(2) School of Mathematics and Statistics, University of Sydney, Sydney, NSW, 2006, Australia |
| Abstract: | This paper investigates weighted approximations for Studentized U-statistics type processes, both with symmetric and antisymmetric kernels, only under the assumption that the distribution of the projection variate is in the domain of attraction of the normal law. The classical second moment condition E|h(X 1, X 2)|2 < ∞ is also relaxed in both cases. The results can be used for testing the null assumption of having a random sample versus the alternative that there is a change in distribution in the sequence. |
| Keywords: | KeywordHeading" > and phrases weighted approximations in probability functional limit theorems U-statistics type processes Studentization change in distribution symmetric and antisymmetric kernels Gaussian processes |
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