Displaying similar documents to “Large deviations for quasi-arithmetically self-normalized random variables”

A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics

Michael H. Neumann (2013)

ESAIM: Probability and Statistics

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We derive a central limit theorem for triangular arrays of possibly nonstationary random variables satisfying a condition of weak dependence in the sense of Doukhan and Louhichi [84 (1999) 313–342]. The proof uses a new variant of the Lindeberg method: the behavior of the partial sums is compared to that of partial sums of Gaussian random variables. We also discuss a few applications in statistics which show that our central limit theorem is tailor-made for statistics of different type. ...

The local relaxation flow approach to universality of the local statistics for random matrices

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...

Moderate deviations for two sample t-statistics

Hongyuan Cao (2007)

ESAIM: Probability and Statistics

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Let be a random sample from a population with mean and variance σ 1 2 , and be a random sample from another population with mean and variance σ 2 2 independent of {}. Consider the two sample t-statistic T = X ¯ - Y ¯ - ( μ 1 - μ 2 ) s 1 2 / n 1 + s 2 2 / n 2 . This paper shows that ln ²/2 for any satisfying → ∞, as provided 0 < < ∞. If, in addition, , , then P ( T ≥ x ) 1 - Φ ( x ) → 1 holds uniformly in

The emergence of french probabilistic statistics. Borel and the Institut Henri Poincaré around the 1920s

Rémi Catellier, Laurent Mazliak (2012)

Revue d'histoire des mathématiques

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This paper concerns the emergence of modern mathematical statistics in France after the First World War. Emile Borel’s achievements are presented, and especially his creation of two institutions where mathematical statistics was developed: the , (ISUP) in 1922 and above all the (IHP) in 1928. At the IHP, a new journal was created in 1931. We discuss the first papers in that journal dealing with mathematical statistics.

Asymptotic behavior of the Empirical Process for Gaussian data presenting seasonal long-memory

Mohamedou Ould Haye (2010)

ESAIM: Probability and Statistics

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We study the asymptotic behavior of the empirical process when the underlying data are Gaussian and exhibit long-memory. We prove that the limiting process can be quite different from the limit obtained in the case of long-memory. However, in both cases, the limiting process is degenerated. We apply our results to von–Mises functionals and -Statistics.

Quasi-static rate-independent evolutions: characterization, existence, approximation and application to fracture mechanics

Matteo Negri (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We characterize quasi-static rate-independent evolutions, by means of their graph parametrization, in terms of a couple of equations: the first gives stationarity while the second provides the energy balance. An abstract existence result is given for functionals ℱ of class in reflexive separable Banach spaces. We provide a couple of constructive proofs of existence which share common features with the theory of minimizing movements for gradient flows. Moreover, considering...

Five Turning Points in the Historical Progress of Statistics - My Personal Vision

von Collani, Elart (2014)

Serdica Journal of Computing

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Statistics has penetrated almost all branches of science and all areas of human endeavor. At the same time, statistics is not only misunderstood, misused and abused to a frightening extent, but it is also often much disliked by students in colleges and universities. This lecture discusses/covers/addresses the historical development of statistics, aiming at identifying the most important turning points that led to the present state of statistics and at answering the questions “What went...