Estimation of a discrete probability under constraint of κ-monotonicity

摘要

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.