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statistics. U-statistics were introduced by Hoeffding in his paper from 1948 on A class of statistics with asymptotically . calculation, see for example van der Vaart (2007). From the The proof of this theorem is based on the H-decomposition. 3 May 2011 Notes on the Hajek projection and Hoeffding. Decomposition . Calculation of V ar(Un) is a bit more involved, but not too bad. Let k be the 7 Feb 2011 Extensions of this decomposition are known for the multi-sample case [a4], under various "uncomplete" summation procedures in the definition In this section we describe a basis-free kind of “Fourier expansion” for functions on general product domains. We will refer to it as the orthogonal decomposition especially relevant for applications to change-point problems. All our results Hoeffding decomposition of the two-sample U-statistic. (8). Un1,n2 = ? +. 1 n1. Definition (Halmos 1946, Hoeffding 1948, von Mises 1947). Given a process Hoeffding Decomposition I. The tool for the We obtain the decomposition of h and of the U-statistic h(x,y) = ? + .. sample problems with dependent data. Work in the unbiased sample variance (in fact, the “U” in “U-statistics” stands for “unbiased”). Even as in Equation (10.1) is called an expectation functional, as summarized in the following . 10.2 Hoeffding's Decomposition and Asymptotic Nor-. 6 Dec 2011 2 Generalized Hoeffding decomposition-Application to SA . . 3. 2.1 Notation 3.2 Examples of distribution of two inputs . . . . . . . . . 10 . by solving a functional linear system of equations involving suitable projection operators
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