A second Marshall inequality in convex estimation

Fadoua Balabdaoui (1, 2) , Kaspar Rufibach (3)

1 IMS - Institut für Mathematische Stochastik
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 UZH - Universität Zürich [Zürich] = University of Zurich

We prove a second Marshall inequality for adaptive convex density estimation via Least Squares. The result completes the first inequality proved recently by \mycite{duembgen:06}, and is very similar to the original Marshall inequality in monotone estimation.

Mots clés: Convex functions; Marshall inequality; cubic polynomial

Domaines: Théorie [stat.TH]; Statistiques [math.ST]

Fadoua Balabdaoui, Kaspar Rufibach. A second Marshall inequality in convex estimation. 2007. ⟨hal-00363236⟩