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- W3149019712 abstract "Part 1 Basic definitions: one sample of UB-statistics multi-sample UB-statistics Von Mises' statistics Banach-valued symmetric statistics permanent symmetric statistics multiple stochastic integrals B-valued polynomial chaos. Part 2 Inequalities: inqualities based on the Hoeffding formula Martingale moment inequalities maximal inequalities contraction and symmetrization inequalities de-coupling inequalities hypercontractive method in moment inequalities moment inequalities in Banach spaces of type r. Part 3 Law of large numbers: one-sample theorem convergence to a chaos multi-sample UB-statistics Poisson approximation stable approximation approximation with increasing degrees symmetric statistics U-statistics with varying kernels weighted U-statistics. Part 4 Functional limit theorems: non-degenerate kernels degenerate kernels weak convergence to a chaos process weak convegence in the Poisson approximation scheme invariance principle for symmetric statistics functional limit theorems with varying kernels weak convergence of U-processes. Paqrt 5 Approximation estimates: general methods of estimation rate of normal approximation of UR-statistics estimates with increasing degree non-uniform estimates rate of chaos approximation normal approximation of UH-statistics multiple-sample UH-statistics estimates in central limit theorem i2r rate of Poisson approximation. Part 6 Asymptotic expansions. Part 7 Large deviations. Part 8 Law of iterated logarithm. Part 9 Dependent variables. (Part contents)" @default.
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- W3149019712 date "1996-12-31" @default.
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- W3149019712 title "U-Statistics in Banach Spaces" @default.
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- W3149019712 doi "https://doi.org/10.1515/9783112318898" @default.
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