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arXiv · 2607.26065

When Kernel Ridge Regression Meets the H\"older-Zygmund Class: Minimax Optimality and Failure of Properness

Yuxuan Hou
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Abstract

We study kernel ridge regression for nonparametric regression over the H\"older-Zygmund class. Using an RKHS equivalent to a Sobolev space of smoothness s+d/2, we prove that misspecified KRR attains the minimax L2 rate n^{-2s/(2s+d)}. We also show that properness fails in the H\"older-Zygmund norm: even for the zero regression function with Gaussian noise, the expected squared H\"older-Zygmund norm of the KRR noise component grows as log n.

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Yuxuan Hou. 2026-06-19. When Kernel Ridge Regression Meets the H\"older-Zygmund Class: Minimax Optimality and Failure of Properness. https://arxiv.org/abs/2607.26065

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