About projections of logarithmic Sobolev inequalities
About the stationary states of vortex systems
Adaptive estimation of a quadratic functional of a density by model selection
We consider the problem of estimating the integral of the square of a density from the observation of a sample. Our method to estimate is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for -statistics of order 2 due to Houdré and Reynaud.
Adaptive estimation of a quadratic functional of a density by model selection
We consider the problem of estimating the integral of the square of a density f from the observation of a n sample. Our method to estimate is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for U-statistics of order 2 due to Houdré and Reynaud.
Adaptive goodness-of-fit testing from indirect observations
In a convolution model, we observe random variables whose distribution is the convolution of some unknown density f and some known noise density g. We assume that g is polynomially smooth. We provide goodness-of-fit testing procedures for the test H0: f=f0, where the alternative H1is expressed with respect to -norm (i.e. has the form ). Our procedure is adaptive with respect to the unknown smoothness parameterτ of f. Different testing rates (ψn) are obtained according to whether f0 is polynomially...
Adaptive hard-thresholding for linear inverse problems
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. These filter methods are generally restricted to monotonic transformations, e.g. the Tikhonov regularization or the spectral cut-off. However, in several cases, non-monotonic sequences of filters may appear more appropriate. In this paper, we study a hard-thresholding regularization method that extends the spectral cut-off procedure to non-monotonic sequences....
Almost Higher Order Stochastic Dominance
In this paper, we develop the concept of almost stochastic dominance for higher order preferences and investigate the related properties of this concept.
An application of multivariate total positivity to peacocks
We use multivariate total positivity theory to exhibit new families of peacocks. As the authors of [F. Hirsch, C. Profeta, B. Roynette and M. Yor, Peacocks and associated martingales vol. 3. Bocconi-Springer (2011)], our guiding example is the result of Carr−Ewald−Xiao [P. Carr, C.-O. Ewald and Y. Xiao, Finance Res. Lett. 5 (2008) 162–171]. We shall introduce the notion of strong conditional monotonicity. This concept is strictly more restrictive than the conditional monotonicity as defined in [F....
An exponential inequality for negatively associated random variables.
An extension of Billingsley’s uniform boundedness theorem to higher-dimensional -processes
An extension of Chebyshev's inequality
An extension of Stolarsky means.
An Improved General Stochastic Inequality
An inequality about -Series.
An inequality for the asymmetry of distributions and a Berry-Esseen theorem for random summation.
An inequality for the predictable projection of an adapted process
An integral analogue of the Ostrowski inequality.
An Introduction to the Theory of Stochastic Orders.
An isoperimetric inequality on the ℓp balls
The normalised volume measure on the ℓnp unit ball (1≤p≤2) satisfies the following isoperimetric inequality: the boundary measure of a set of measure a is at least cn1/pãlog1−1/p(1/ã), where ã=min(a, 1−a).
An observation about submatrices.