Estimation de densités unimodales

This paper proposes a new nonparametric unimodal estimator of a unimodal probability density function, in the case where the mode is known. The classical solution to this problem is the maximum-likelihood estimator under monotonicity constraint, considered by Grenander (1956). Our approach is based on a unimodal rearrangement of the kernel estimator of the density. Asymptotic properties of this estimator are studied, and its small-sample behaviour is examined through simulations.