The LIL for U-Statistics in Hilbert Spaces |
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| Authors: | Radosław Adamczak Rafał Latała |
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| Affiliation: | (1) Institute of Mathematics, Polish Academy of Sciences, P.O. Box 21, Sniadeckich 8, Warszawa, Poland;(2) Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland |
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| Abstract: | We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for U-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued U-statistics of arbitrary order, which are of independent interest. R. Adamczak’s research partially supported by MEiN Grant 2 PO3A 019 30. R. Latała’s research partially supported by MEiN Grant 1 PO3A 012 29. |
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| Keywords: | U-statistics Tail and moment estimates Law of the iterated logarithm |
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