A second Marshall inequality in convex estimation

We prove a second Marshall inequality for adaptive convex density estimation via least squares. The result completes the first inequality proved recently by Dümbgen et al. [2007. Marshall's lemma for convex density estimation. IMS Lecture Notes-Monograph Series, submitted for publication. Preprint available at 〈http://arxiv.org/abs/math.ST/0609277〉], and is very similar to the original Marshall inequality in monotone estimation.