Jiménez Rugama, Lluís Antoni Gilquin, Laurent

In the field of sensitivity analysis, Sobol’ indices are sensitivity measures widely used to assess the importance of inputs of a model to its output. The estimation of these indices is often performed trough Monte Carlo or quasi-Monte Carlo methods. A notable method is the replication procedure that estimates first-order indices at a reduced cost ...

Vera, Matias Rey Vega, Leonardo Piantanida, Pablo

This paper investigates a multi-terminal source coding problem under a logarithmic loss fidelity which does not necessarily lead to an additive distortion measure. The problem is motivated by an extension of the Information Bottleneck method to a multi-source scenario where several encoders have to build cooperatively rate-limited descriptions of t...

Nguyen, Thi Ngoc Minh Le Corff, Sylvain Moulines, Eric

A prevalent problem in general state space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous analysis of such approximations of smoothed distributions provided by the two-filter algorithms. We extend the resu...

Lerasle, Matthieu Szabó, Zoltán Massiot, Gaspar Moulines, Eric

Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy ; also called N-distance or energy distance), with numerous successful applications. The representation is constructed as the expectation of the feature map...

Comte, Fabienne Duval, Céline

We consider nonparametric density estimation for interarrival times density of a renewal process. If it is possible to get continuous observation of the process, then a projection estimator in an orthonormal functional basis can be built; we choose to work on R+ with the Laguerre basis. Nonstandard decompositions can lead to bounds on the mean inte...

Ouni, Zaïd Denis, Christophe Chauvel, Cyril Chambaz, Antoine

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Maume-Deschamps, Véronique Niang, Ibrahima

The paper concerns quantile oriented sensitivity analysis. We rewrite the corresponding indices using the Conditional Tail Expectation risk measure. Then, we use this new expression to built estimators.

Alvarez-Andrade, Sergio Bouzebda, Salim Lachal, Aimé

The main purpose of this paper is to investigate the strong approximation of the $p$-fold integrated empirical process, $p$ being a fixed positive integer. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer process. Our arguments are based in part on results of Koml\'os, M...

Proïa, Frédéric Soltane, Marius

A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, then we give the second-order stationarity conditions and the autocorrelation function of the process. Then we study some asymptotic properties of the empirical mean an...

Georg, Pichler Piantanida, Pablo MATZ, Gerald

Let (Xn,Yn) denote n independent, identically distributed copies of two arbitrarily correlated Rademacher random variables (X,Y) on {−1,1}. We prove that the inequality I(f(Xn);g(Yn))≤I(X;Y) holds for any two Boolean functions: f,g:{−1,1}n→{−1,1} (I(⋅;⋅) denotes mutual information.) We further show that equality in general is achieved only by the d...