# Targeted Estimation of L2 Distance Between Densities and its Application to Geo-spatial Data

## TL;DR

This paper introduces a targeted maximum likelihood estimator for the L2 distance between two probability densities, demonstrating improved accuracy and confidence interval coverage over kernel density estimation in geo-spatial data analysis.

## Contribution

The paper proposes a novel targeted maximum likelihood estimator for the L2 distance, outperforming kernel density estimation in accuracy and reliability.

## Key findings

- Superior confidence interval coverage compared to kernel methods
- Lower mean squared error in estimating L2 distance
- Effective application to geo-spatial data analysis

## Abstract

We examine the integrated squared difference, also known as the L2 distance (L2D), between two probability densities. Such a distance metric allows for comparison of differences between pairs of distributions or changes in a distribution over time. We propose a targeted maximum likelihood estimator for this parameter based on samples of independent and identically distributed observations from both underlying distributions. We compare our method to kernel density estimation and demonstrate superior performance for our method with regards to confidence interval coverage rate and mean squared error.