On Hilbert-Space-Valued U-Statistics
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Theory of Probability & Its Applications
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Abstract
In this note we show that an elementary argument similar to the one used in [1] for real-valued $U$-statistics can be applied to Hilbert-space-valued $U$-statistics to obtain the rate of convergence of their distributions to their Gaussian limits.
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Puri, M. L. "On Hilbert space valued U-statistics." Translated by SIAM, Theory of Probability and Its Applications (1991), Volume 36 Issue 3, 619-621. Co-author: V.V. Sazonov.