A Weak Invariance Principle for Weighted U-Statistics with Varying Kernels

T. Mikosch

Journal of Multivariate Analysis, 1993, vol. 47, issue 1, 82-102

Abstract: We prove limit theorems of functional type for weighted U-statistics with varying kernel. In particular, we show that the Lévy-Prokhorov distance between these processes un and certain processes vn constructed from i.i.d. standard normal variables converges to zero. Limit results for un follow then from the corresponding ones for vn.

Date: 1993
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