Convergence of U-statistics for interacting particle systems

Abstract : The convergence of U-statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the independence assumption is crucial (Lee in Statistics: Textbooks and Monographs, vol. 10, Dekker, New York, 1990; de la Peña and Giné in Decoupling. Probability and Its Application, Springer, New York, 1999). When dealing with Feynman-Kac and other interacting particle systems of Monte Carlo type, one faces a new type of problem. Namely, in a sample of N particles obtained through the corresponding algorithms, the distributions of the particles are correlated--although any finite number of them is asymptotically independent with respect to the total number N of particles. In the present article, exploiting the fine asymptotics of particle systems, we prove convergence theorems for U-statistics in this framework
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Contributor : Sylvain Rubenthaler <>
Submitted on : Friday, September 27, 2013 - 12:06:45 PM
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Sylvain Rubenthaler, Pierre Del Moral, Frédéric Patras. Convergence of U-statistics for interacting particle systems. Journal of Theoretical Probability, Springer, 2011, 24 (4), pp.1002-1027. ⟨10.1007/s10959-011-0355-6⟩. ⟨hal-00866889⟩



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