Tze Leng Lai, Qi-Man Shao, Qiying Wang (2011)
ESAIM: Probability and Statistics
Similarity:
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
Similarity:
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
Similarity:
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...