Bagging of Density Estimators

TL;DR

This paper introduces new density estimators created by averaging classical estimators over bootstrap samples, demonstrating their consistency and providing methods for non-parametric confidence intervals.

Contribution

It presents novel density estimators based on bootstrap averaging, proves their L2-consistency, and offers a way to construct non-parametric confidence intervals.

Findings

The new estimators are L2-consistent.

Simulations show competitive performance.

Method for non-parametric confidence intervals is effective.

Abstract

In this work we give new density estimators by averaging classical density estimators such as the histogram, the frequency polygon and the kernel density estimators obtained over different bootstrap samples of the original data. We prove the L 2-consistency of these new estimators and compare them to several similar approaches by extensive simulations. Based on them, we give also a way to construct non parametric pointwise confidence intervals for the target density.