Estimating a monotone probability mass function with known flat regions

TL;DR

This paper introduces a new estimator for a discrete monotone probability mass function with known flat regions, analyzing its asymptotic properties and comparing it to existing estimators like Grenander and monotone rearrangement.

Contribution

The paper presents a novel estimator tailored for monotone pmfs with known flat regions, enhancing estimation accuracy over traditional methods.

Findings

The new estimator performs better than Grenander in simulations.

Asymptotic analysis shows desirable convergence properties.

Comparison indicates improved estimation in flat regions.

Abstract

We propose a new estimator of a discrete monotone probability mass function with known flat regions. We analyse its asymptotic properties and compare its performance to the Grenander estimator and to the monotone rearrangement estimator.