Tze Leng Lai, Qi-Man Shao, Qiying Wang (2011)
ESAIM: Probability and Statistics
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Let be a Studentized U-statistic. It is proved that a Cramér type moderate deviation ( ≥ )/(1 − Φ()) → 1 holds uniformly in ∈ [0, ( )) when the kernel satisfies some regular conditions.
László Erdős, Benjamin Schlein, Horng-Tzer Yau, Jun Yin (2012)
Annales de l'I.H.P. Probabilités et statistiques
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We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides with the local statistics of the corresponding Gaussian ensemble provided the distribution of the individual matrix element is smooth and the eigenvalues { }=1 are close to their classical location { }=1 determined by the...
Jean-Louis Bon, Eugen Păltănea (2005)
ESAIM: Probability and Statistics
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The paper is motivated by the stochastic comparison of the reliability of non-repairable -out-of- systems. The lifetime of such a system with nonidentical components is compared with the lifetime of a system with identical components. Formally the problem is as follows. Let be positive independent random variables with common distribution . For λ > 0 and µ > 0, let consider and . Remark that this is no more than a change of scale for each term. For , let us define to be the...
Antonio Cuevas, Ricardo Fraiman, László Györfi (2013)
ESAIM: Probability and Statistics
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We deal with a subject in the interplay between nonparametric statistics and geometric measure theory. The measure () of the boundary of a set ⊂ ℝ (with ≥ 2) can be formally defined, a simple limit, by the so-called Minkowski content. We study the estimation of () from a sample of random points inside and outside . The sample design assumes that, for each sample point, we know (without error) whether or not that point belongs to . Under this design we...
Bernardo Galvão-Sousa (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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The behavior of energy minimizers at the boundary of the domain is of great importance in the Van de Waals-Cahn-Hilliard theory for fluid-fluid phase transitions, since it describes the effect of the container walls on the configuration of the liquid. This problem, also known as the liquid-drop problem, was studied by Modica in [ 4 (1987) 487–512], and in a different form by Alberti in [ is a scalar density function and and are double-well potentials, the exact scaling...