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Journal of Mathematical Physics, 2010 The notion of a U-statistic for an n-tuple of identical quantum systems is introduced in analogy to the classical (commutative) case: given a self-adjoint “kernel” K acting on (Cd)⊗r with r<n, we define the symmetric operator Un=(nr)∑βK(β) with K(β) being the kernel acting on the subset β of {1,…,n}.
Madalin Guta, Christina Butucea
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Self-Normalized Moderate Deviations for Degenerate U-Statistics [PDF]
EntropyIn this paper, we study self-normalized moderate deviations for degenerate U-statistics of order 2. Let {Xi,i≥1} be i.i.d. random variables and consider symmetric and degenerate kernel functions in the form h(x,y)=∑l=1∞λlgl(x)gl(y), where λl>0, Egl(X1)=0,
Lin Ge, Hailin Sang, Qi-Man Shao
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Renewal theory for asymmetric $U$-statistics
Electronic Journal of Probability, 2018 We extend a functional limit theorem for symmetric $U$-statistics [Miller and Sen, 1972] to asymmetric $U$-statistics, and use this to show some renewal theory results for asymmetric $U$-statistics. Some applications are given.
Svante Janson
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A new method for determining geochemical anomalies: U-N and U-A fractal models [PDF]
International Journal of Mining and Geo-Engineering, 2022 Undoubtedly, determining the threshold of anomalies and separating geochemical anomalies from background is one of the most important stages of minerals exploration.
Seyyed saeed Ghannadpour +1 more
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Graphs defined on groups [PDF]
International Journal of Group Theory, 2022 This paper concerns aspects of various graphs whose vertex set is a group $G$ and whose edges reflect group structure in some way (so that, in particular, they are invariant under the action of the automorphism group of $G$).
Peter J. Cameron
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Muth Distribution and Estimation of a Parameter Using Order Statistics
Statistica, 2021 In this work, we have considered a lifetime distribution namely Muth distribution and pointed out instances where it appears as a good model to study the stochastic nature of the variable under consideration.
Muhammed Rasheed Irshad +2 more
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DESIGN BASED INCOMPLETE U-STATISTICS [PDF]
Statistica Sinica, 2021 49 ...
Kong, Xiangshun, Zheng, Wei
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Asymptotic Expansions for Symmetric Statistics with Degenerate Kernels
Mathematics, 2022 Asymptotic expansions for U-statistics and V-statistics with degenerate kernels are investigated, respectively, and the remainder term O(n1−p/2), for some p≥4, is shown in both cases.
Shuya Kanagawa
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Some remarks on the ergodic theorem for $U$-statistics
Comptes Rendus. Mathématique, 2023 In this note, we investigate the convergence of a $U$-statistic of order two having stationary ergodic data. We will find sufficient conditions for the almost sure and $L^1$ convergence and present some counter-examples showing that the $U$-statistic ...
Dehling, Herold +2 more
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On the rate of convergence of degenerate U-statistics
Lietuvos Matematikos Rinkinys, 2005 Let X, X1, X2, ... be independent identically distributed random variables taking values in a measurable space (Ω, ℜ). Let h(x, y) be real valued measurable symmetric function of the arguments x, y ∈ ℜ. Assume that Eh(x, X)= 0, for all x.
Olga Januškevičienė
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