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  • 1 Carleton University School of Mathematics and Statistics 1125 Colonel By Drive Ottawa ON Canada K1S 5B6
  • 2 University of Sydney School of Mathematics and Statistics Sydney NSW 2006 Australia
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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(X1, X2)|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.