# Indiana University

 dc.contributor.author Borovskikh, Yu. V. dc.contributor.author Puri, Madan L. dc.contributor.author Sazonov, V. V. dc.date.accessioned 2018-05-03T18:31:43Z dc.date.available 2018-05-03T18:31:43Z dc.date.issued 1997 dc.identifier.citation Puri, M. L. “Normal approximation of U-statistics in Hilbert spaces.” Translation by SIAM,Theory of Probability and its Applications (1997), Volume 41 Issue 3, 481–504. Co-authors: Yu.V. Borovskich and V.V. Sazonov. en dc.identifier.uri http://hdl.handle.net/2022/22086 dc.description Publisher's, offprint version en dc.description.abstract Let $\{U_n\}$, $n=1,2,...,$ be Hilbert space H-valued U-statistics with kernel $\Phi(\cdotp,\cdot)$, corresponding to a sequence of observations (random variables) $X_1,X_2,\ldots\$. The rate of convergence on balls in the central limit theorem for $\{U_n\}$ is investigated. The obtained estimate is of order $n^{-1/2}$ and depends explicitly on $E\|\Phi(X_1,X_2)\|^3$ and on the trace and the first nine eigenvalues of the covariance operator of $E(\Phi(X_1,X_2)|X_1)$. en dc.language.iso en en dc.publisher Theory of Probability & Its Applications en dc.relation.isversionof https://epubs.siam.org/doi/10.1137/S0040585X97975198 en dc.subject U-statistic en dc.subject Hilbert space en dc.subject central limit theorem en dc.subject normal (Gaussian) approximation en dc.subject rate of convergence en dc.title Normal Approximation of U-Statistics in Hilbert Space en dc.type Article en dc.identifier.doi 10.1137/S0040585X97975198
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