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We study additive regression under a potentially non-product random design on $[0,1]^d$, allowing the dimension $d$ to grow with the sample size $n$.
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We study additive regression under a potentially non-product random design on $[0,1]^d$, allowing the dimension $d$ to grow with the sample size $n$. We introduce coupled smoothness classes that separately control the regularity of the marginal densities and the density-weighted additive components. To handle dependence, we adapt a Riesz-basis construction for functional ANOVA models and establish compatibility bounds with constants independent of the dimension under uniform bounds on the joint density. We construct thresholded least-squares estimators and establish matching minimax upper and...
Discovered via ArXiv
Research papers and preprints from arXiv.
Publisher: arxiv.org
ID: http://arxiv.org/abs/2609.39212v1 · Indexed about 1 hour ago