Marshall's lemma for convex density estimation
Lutz Duembgen, Kaspar Rufibach, Jon A. Wellner
Abstract
Marshall's [Nonparametric Techniques in Statistical Inference (1970) 174--176] lemma is an analytical result which implies n--consistency of the distribution function corresponding to the Grenander [Skand. Aktuarietidskr. 39 (1956) 125--153] estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on [0,∞).
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