Minimum Local Distance Density Estimation

TL;DR

This paper introduces a local density estimator based on minimum sample distances, which uses subset division and offers smoother estimates than nearest-neighbor methods, with proven asymptotic properties and competitive convergence.

Contribution

The paper proposes a novel density estimation method based on first order statistics that uses subset division, providing smoother estimates and asymptotic analysis.

Findings

Provides good density estimates across various distributions

Offers smoother estimates compared to nearest-neighbor methods

Demonstrates competitive convergence properties

Abstract

We present a local density estimator based on first order statistics. To estimate the density at a point, $x$, the original sample is divided into subsets and the average minimum sample distance to $x$ over all such subsets is used to define the density estimate at $x$. The tuning parameter is thus the number of subsets instead of the typical bandwidth of kernel or histogram-based density estimators. The proposed method is similar to nearest-neighbor density estimators but it provides smoother estimates. We derive the asymptotic distribution of this minimum sample distance statistic to study globally optimal values for the number and size of the subsets. Simulations are used to illustrate and compare the convergence properties of the estimator. The results show that the method provides good estimates of a wide variety of densities without changes of the tuning parameter, and that it offers competitive convergence performance.