Estimation of a discrete probability under constraint of κ-monotonicity

Jade Giguelay (1)

1 MaIAGE - Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas]

We propose two least-squares estimators of a discrete probability under the constraint of k-monotonicity and study their statistical properties. We give a characterization of these estimators based on the decomposition on a spline basis of k-monotone sequences. We develop an algorithm derived from the Support Reduction Algorithm and we finally present a simulation study to illustrate their properties. MSC 2010 subject classifications: Least squares, non-parametric estimation, k-monotone discrete probability, shape constraint, Support Reduction Algorithm.

Domaines: Sciences du Vivant [q-bio]

Jade Giguelay. Estimation of a discrete probability under constraint of κ-monotonicity. Electronic Journal of Statistics , 2017, 11, pp.1-49. ⟨10.1214/16-EJS1220⟩. ⟨hal-01601603⟩