Estimation of a discrete probability under constraint of $k$-monotonicity

Abstract

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.