The subject of this paper is to estimate adaptively the common probability density of n independent, identically distributed random variables. The estimation is done at a fixed point x0 E R, over the density functions that belong to the Sobolev class Wn (B,L). We consider the adaptive problem...

We estimate the common density function of n i.i.d. observations, at a fixed point, over Sobolev classes of functions having regularity B. We prove that the optimal rate of convergence cannot be attained in adaptive estimation, i.e. uniformly over B in some interval B. A logarithmically slower...

We derive sharp asymptotic minimax bounds (that is, bounds which concern the exact asymptotic constant of the risk) for nonparametric density estimation based on weakly dependent observations. We study two particular problems for which there already exist such results in the case of independent...

We consider density pointwise estimation in the i.i.d. case and look for bewst attainable asumptotic rates of convergence. The problem is adaptive, which means that the regularity parameter, b, describing the class of densities, varies in a set B.

We consider copulas with a given diagonal section and compute the explicit density of the unique optimal copula which maximizes the entropy. In this sense, this copula is the least informative among the copulas with a given diagonal section. We give an explicit criterion on the diagonal section...

We consider density pointwise estimation and look for best attainable asymptotic rates of convergence. The problem is adaptive, which means that the regularity parameter, Ø, describing the class of densities, varies in a set B. We shall consider, successively, two classes of densities, issued...

We give here a simulation study of a density estimator, issued from sharp adaptive estimation. This nonparametric estimator was previously proved to have interesting theoretical properties. In this paper we describe the method and apply it successfully to i.i.d. simulated data issued from...