Shape constrained kernel density estimation - Melanie Birke (Technische Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen, 2008)
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 the resulting estimate is a density itself and shares the asymptotic properties of the unconstrained estimate. A short simulation study shows the ?nite sample behavior.
Keywords: 519; Convexity; log-concavity; monotone rearrangements; monotonicity; nonparametric density estimation