Optimal Kernel for Kernel-Based Modal Statistical Methods

• URL: http://arxiv.org/abs/2304.10046v1
• Date: Thu, 20 Apr 2023 01:47:35 GMT
• Title: Optimal Kernel for Kernel-Based Modal Statistical Methods
• Authors: Ryoya Yamasaki and Toshiyuki Tanaka
• Abstract summary: Kernel-based modal statistical methods include mode estimation, regression, and clustering. We study effect of the selection of the kernel function to estimation accuracy of these methods.
• Score: 8.571896191090744
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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