# Optimal Kernel for Kernel-Based Modal Statistical Methods

arXiv: https://arxiv.org/abs/2304.10046 · HTML: https://mlsanity.com/paper/2304.10046/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 37 references that are in the map.
- First posted on arXiv 20 Apr 2023.

## Builds on (most cited first, 3 of 3)

- [Kernel Selection for Modal Linear Regression: Optimal Kernel and IRLS Algorithm](https://mlsanity.com/paper/2001.11168/) (2020)
- [Modal Principal Component Analysis](https://mlsanity.com/paper/2008.03400/) (2020)
- [Modal clustering asymptotics with applications to bandwidth selection](https://mlsanity.com/paper/1901.07300/) (2019)

## Built on by (most cited first, 2 of 2)

- [Convergence Analysis of Mean Shift](https://mlsanity.com/paper/2305.08463/) (2023)
- [Convergence Analysis of Blurring Mean Shift](https://mlsanity.com/paper/2402.15146/) (2024)

## Abstract (arXiv)

Kernel-based modal statistical methods include mode estimation, regression, and clustering. Estimation accuracy of these methods depends on the kernel used as well as the bandwidth. We study effect of the selection of the kernel function to the estimation accuracy of these methods. In particular, we theoretically show a (multivariate) optimal kernel that minimizes its analytically-obtained asymptotic error criterion when using an optimal bandwidth, among a certain kernel class defined via the number of its sign changes.