# Kernel Selection for Modal Linear Regression: Optimal Kernel and IRLS Algorithm

arXiv: https://arxiv.org/abs/2001.11168 · HTML: https://mlsanity.com/paper/2001.11168/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2020.

## Built on by (most cited first, 3 of 3)

- [Convergence Analysis of Mean Shift](https://mlsanity.com/paper/2305.08463/) (2023)
- [Optimal Kernel for Kernel-Based Modal Statistical Methods](https://mlsanity.com/paper/2304.10046/) (2023)
- [Convergence Analysis of Blurring Mean Shift](https://mlsanity.com/paper/2402.15146/) (2024)

## Abstract (arXiv)

Modal linear regression (MLR) is a method for obtaining a conditional mode predictor as a linear model. We study kernel selection for MLR from two perspectives: "which kernel achieves smaller error?" and "which kernel is computationally efficient?". First, we show that a Biweight kernel is optimal in the sense of minimizing an asymptotic mean squared error of a resulting MLR parameter. This result is derived from our refined analysis of an asymptotic statistical behavior of MLR. Secondly, we provide a kernel class for which iteratively reweighted least-squares algorithm (IRLS) is guaranteed to converge, and especially prove that IRLS with an Epanechnikov kernel terminates in a finite number of iterations. Simulation studies empirically verified that using a Biweight kernel provides good estimation accuracy and that using an Epanechnikov kernel is computationally efficient. Our results improve MLR of which existing studies often stick to a Gaussian kernel and modal EM algorithm specialized for it, by providing guidelines of kernel selection.