# Recursive density estimators based on Robbins-Monro's scheme and using Bernstein polynomials

## TL;DR

This paper introduces a recursive density estimator using Robbins-Monro's algorithm and Bernstein polynomials, addressing boundary issues and demonstrating its effectiveness through theoretical analysis and empirical validation.

## Contribution

It presents a novel recursive density estimator that alleviates boundary problems, with proven asymptotic properties and validated performance against existing methods.

## Key findings

- The estimator effectively handles boundary bias.
- Theoretical asymptotic properties are established.
- Simulation and real data confirm improved performance.

## Abstract

In this paper, we consider the alleviation of the boundary problem when the probability density function has bounded support. We apply Robbins-Monro's algorithm and Bernstein polynomials to construct a recursive density estimator. We study the asymptotic properties of the proposed recursive estimator. We then compared our proposed recursive estimator with many others estimators. Finally, we confirm our theoretical result through a simulation study and then using two real datasets.