In this paper we discuss consistency of the posterior distribution in cases where the Kullback-Leibler condition is not verified. This condition is stated as : for all $\epsilon 0$ the prior probability of sets in the form $\{f ; KL(f0 , f ) \leq \epsilon\}$ where KL(f0 , f ) denotes the...

In the context of nonparametric Bayesian estimation a Markov chain Monte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional diffusion. The drift is modeled by a scaled linear...

Purpose - This paper aims mainly at introducing applied statisticians and econometricians to the current research methodology with non-Euclidean data sets. Specifically, it provides the basis and rationale for statistics in Wasserstein space, where the metric on probability measures is taken as...

Purpose - This paper aims to offer a tutorial/introduction to new statistics arising from the theory of optimal transport to empirical researchers in econometrics and machine learning. Design/methodology/approach - Presenting in a tutorial/survey lecture style to help practitioners with the...

In stochastic optimization models the underlying probability measure must be very often replaced by its approximations. This leads to the investigation of the stability of such models with respect to changes in the probability measure. In this context, special attention is paid to recourse...

Optimization techniques enter often as a mathematical tool into many economic applications. In these models, uncertainty is modelled via probability distribution that is approximated or estimated in real cases. Then we ask for a stability of solutions with respect to changes in the probability...

<p><span style="font-size: 11.000000pt; font-family: 'CMR10';">In this paper, we aim to explore the speed of convergence of the Wasserstein distance between stable cumulative distribution functions and their empirical counterparts. The theoretical results are compared with the results provided by simulations. The need to use simulations is explained by the...</span></p>

The subject of this paper is the estimation of a probability measure on Rd from the data observed with an additive noise, under the Wasserstein metric of order p (with p≥1). We assume that the distribution of the errors is known and belongs to a class of supersmooth distributions, and we give...