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Marshall's lemma for convex density estimation

Lutz Duembgen·Kaspar Rufibach·Jon A. Wellner
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Abstract

Marshall's [Nonparametric Techniques in Statistical Inference (1970) 174--176] lemma is an analytical result which implies $\sqrt{n}$--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 $[0,\infty)$.

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Lutz Duembgen, Kaspar Rufibach, Jon A. Wellner. 2006-09-11. Marshall's lemma for convex density estimation. https://doi.org/10.1214/074921707000000292

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