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We study soft threshold estimates of the non-centrality parameter ξ of a non-central χ2 d(ξ) distribution, of interest, for example, in estimation of the squared length of the mean of a Gaussian ve...
We show that empirical risk minimization procedures and regularized empirical risk minimization procedures satisfy nonexact oracle inequalities in an unbounded framework, under the assumption that the...
We consider the problem of estimating a function $f_{0}$ in logistic regression model. We propose to estimate this function $f_{0}$ by a sparse approximation build as a linear combinaison of elements ...
Abstract: The Dvoretzky--Kiefer--Wolfowitz (DKW) inequality says that if $F_n$ is an empirical distribution function for variables i.i.d.\ with a distribution function $F$, and $K_n$ is the Kolmogorov...
In this paper we study the asymptotic behavior of the solu-tion of quasilinear parametric variational inequalities posed in a cylinder with a thin neck, and we obtain the limit problem.
Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions are well known. We give here the correspondance (with quantitative results) for reversible diffusion...
In this paper, by the Chebyshev-type inequalities we define three mappings, investigate their main properties, give some refinements for Chebyshev-type inequalities, obtain some applications.

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