Marshall's lemma for convex density estimation

Details Marshall's lemma for convex density estimation Marshall's lemma for convex density estimation

2006-09-11

arxiv.org/abs/math/0609277v2

IMS Lecture Notes Monograph Series 2007, Vol. 55, 101-107

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921707000000292 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/p

Scientific paper

10.1214/074921707000000292

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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