Estimation of a discrete probability under constraint of k-monotony

TL;DR

This paper introduces two least-squares estimators for discrete probabilities constrained by k-monotony, analyzing their properties, developing an algorithm, and demonstrating their effectiveness through simulations.

Contribution

It presents novel estimators for k-monotone discrete probabilities, with a characterization, an algorithm, and a simulation study to validate their performance.

Findings

Estimators satisfy k-monotony constraints.

Algorithm effectively computes the estimators.

Simulation confirms desirable statistical properties.

Abstract

We propose two least-squares estimators of a discrete probability under the constraint of k-monotony 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.