Résumé
This manuscript, proposes a new nonparametric method for estimating the probability density function. This estimation method combines the Schwartz distribution theory and the possibility theory. It is an extension of the kernel density estimator that leads to imprecise estimation. It is based on a new method for modeling neighborhood. The interval valued estimate it produces is a convex envelope of the Parzen-Rosenblatt estimates obtained with kernels belonging to a coherent convex family. We prove some theoretical properties of this new method. Among these properties, we have shown a kind of convergence of this estimator. We also shown a particular aptitude of this estimator to quantify the error due to random variation in observation. We also propose very low complexity algorithms to compute the proposed methods.