Results 11 to 20 of about 4,122,773 (336)
The LIL for U-Statistics in Hilbert Spaces [PDF]
Journal of Theoretical Probability, 2007 We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for $U$-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued $U$-statistics of arbitrary order, which are of independent interest.
Radosław Adamczak, Rafał Latała
core +6 more sources
Kaplan-Meier V- and U-statistics [PDF]
Electronic Journal of Statistics, 2018 In this paper, we study Kaplan-Meier V- and U-statistics respectively defined as $\theta(\widehat{F}_n)=\sum_{i,j}K(X_{[i:n]},X_{[j:n]})W_iW_j$ and $\theta_U(\widehat{F}_n)=\sum_{i\neq j}K(X_{[i:n]},X_{[j:n]})W_iW_j/\sum_{i\neq j}W_iW_j$, where $\widehat{
Tamara Fern'andez, Nicolás Rivera
semanticscholar +9 more sources
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
openaire +6 more sources
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
openaire +7 more sources
On weighted U-statistics for stationary processes [PDF]
The Annals of Probability, 2004 Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214 ...
Hsing, Tailen, Wu, Wei Biao
openaire +6 more sources
Ranking and Empirical Minimization of U-statistics [PDF]
The Annals of Statistics, 2008 The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. In this paper we formulate the ranking problem in a rigorous statistical framework. The goal is to learn a ranking rule for deciding, among two instances, which one is "better," with minimum ranking risk.
Stephan Clémençon +2 more
openalex +5 more sources
Exponential and Moment Inequalities for U-Statistics [PDF]
, 2000 22 ...
Rafał Latała, Joel Zinn, Evarist Giné
openaire +4 more sources
Renewal theory for asymmetric U-statistics [PDF]
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.
S. Janson
semanticscholar +6 more sources
Revista Colombiana de Estadística, 2017 In this paper, we consider two well-known methods for analysis of the Gini index, which are U-statistics and linearization for some income distributions.
Shahryar Mirzaei +2 more
doaj +2 more sources
AIMS MathematicsIn recent years, there has been a notable shift in focus towards the analysis of non-stationary time series, driven largely by the complexities associated with delineating significant asymptotic behaviors inherent to such processes.
Salim Bouzebda
doaj +2 more sources