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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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Sectorial convergence of U-statistics [PDF]
The Annals of Probability, 2005 Published at http://dx.doi.org/10.1214/009117904000001080 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Gadidov, Anda
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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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U-Statistics in Stochastic Geometry [PDF]
, 2016 This survey will appear as a chapter of the forthcoming book [19]. A U-statistic of order $k$ with kernel $f:\X^k \to \R^d$ over a Poisson process is defined in \cite{ReiSch11} as$$ \sum\_{x\_1, \dots , x\_k \in ^k\_{\neq}} f(x\_1, \dots, x\_k) $$ under appropriate integrability assumptions on $f$.
Lachièze-Rey, Raphaël +1 more
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The LIL for canonical U-statistics
The Annals of Probability, 2008 We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for canonical $U$-statistics of arbitrary order $d$, extending the previously known results for $d=2$. The nasc's are expressed as growth conditions on a parameterized family of norms associated with the $U$-statistics kernel.
Adamczak, Radosław, Latała, Rafał
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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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