In this paper, a method for estimating monotone, convex and log-concave densities is proposed. The estimation procedure consists of an unconstrained kernel estimator which is modi?ed in a second step with respect to the desired shape constraint by using monotone rearrangements. It is shown that...

Proofs for the consistency of the kernel density estimator have historically developed. Four important milestones are the pointwise consistency, the almost sure uniform convergence, the rate of convergence on a bounded interval and the rate of convergence on R. The underlying concepts of total...