k-Nearest neighbor density estimation on Riemannian Manifolds

TL;DR

This paper extends k-nearest neighbor density estimation to data on Riemannian manifolds, analyzing its theoretical properties and demonstrating its practical application through simulations and real data examples.

Contribution

It introduces a novel k-nearest neighbor kernel estimator for Riemannian manifolds and studies its asymptotic properties, with real-world applications.

Findings

Estimator is consistent and asymptotically normal.

Simulation results show good performance of the estimator.

Applications demonstrate the estimator's utility on real manifold data.

Abstract

In this paper, we consider a k-nearest neighbor kernel type estimator when the random variables belong in a Riemannian manifolds. We study asymptotic properties such as the consistency and the asymptotic distribution. A simulation study is also consider to evaluate the performance of the proposal. Finally, to illustrate the potential applications of the proposed estimator, we analyzed two real example where two different manifolds are considered.