Pointwise minimax lower bounds under a multi-index constraint: the price of an unknown orientation
Year: 2026
Type: preprint
Abstract: We consider nonparametric regression with random design and non-Gaussian noise, where the regression function has the multi-index form $F(x)=f(Θx)$ with an unknown link $f:\RR^m\to\RR$ in an anisotropic Hölder class and an unknown matrix $Θ$ with $m\le d$ orthonormal rows. For estimation of $F$ at a fixed point we prove that the minimax risk is bounded from below by a multiple of $L^{1/(2γ+1)}(n^{-1}\ln n)^{γ/(2γ+1)}$, where $γ$ is the harmonic mean of the smoothness indices of the link divided by $m$. For $m
Source: arXiv (Cornell University)
Author: Serdyukova, Nora
Institution: University of Concepción
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221960526