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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...
General nonexact oracle inequalities for classes with a subexponential envelope
Statistical learning fast rates of convergence oracle inequalities regularization classification aggregation model selection
2012/6/21
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...
Non-asymptotic Oracle Inequalities for the Lasso and Group Lasso in high dimensional logistic model
Logistic model Lasso Group Lasso High-dimensional
2012/6/19
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 ...
Dvoretzky--Kiefer--Wolfowitz Inequalities for the Two-sample Case
Kolmogorov–Smirnov test empirical distribution functions Statistics Theory
2011/9/21
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...
Asymptotic behavior of the solution of quasilinear parametric variational inequalities in a beam with a thin neck
asymptotic behavior quasilinear parametric variational inequality
2011/2/23
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.
Poincaré inequalities and hitting times
Poincar´ e inequalities Lyapunov functions hitting times log-concave measures
2011/2/25
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...
Three Mappings Related to Chebyshev-type Inequalities
Chebyshev-type inequality Monotonicity Refinement
2010/1/22
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.