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High-dimensional gaussian model selection on a gaussian design

Nicolas Verzelen (2010)

Annales de l'I.H.P. Probabilités et statistiques

We consider the problem of estimating the conditional mean of a real gaussian variable Y=∑i=1pθiXi+ɛ where the vector of the covariates (Xi)1≤i≤p follows a joint gaussian distribution. This issue often occurs when one aims at estimating the graph or the distribution of a gaussian graphical model. We introduce a general model selection procedure which is based on the minimization of a penalized least squares type criterion. It handles a variety of problems such as ordered and complete variable selection,...

Hypercontractivity of simple random variables

Paweł Wolff (2007)

Studia Mathematica

The optimal hypercontractivity constant for a natural operator semigroup acting on a discrete finite probability space is established up to a universal factor. The two-point spaces are proved to be the extremal case. The constants obtained are also optimal in the related moment inequalities for sums of independent random variables.

Hyper-dependence, hyper-ageing properties and analogies between them: a semigroup-based approach

Rachele Foschi (2013)

Kybernetika

In previous papers, evolution of dependence and ageing, for vectors of non-negative random variables, have been separately considered. Some analogies between the two evolutions emerge however in those studies. In the present paper, we propose a unified approach, based on semigroup arguments, explaining the origin of such analogies and relations among properties of stochastic dependence and ageing.

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