Nearly-minimax variance estimation under rough random design

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Publication Details

Journal
UNC Libraries
Published
2026-09-10
DOI
https://doi.org/10.17615/4qgm-bs81
Primary Topic
Statistical Methods and Inference
Type
article
Field-Weighted Citation Impact
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article

Nearly-minimax variance estimation under rough random design

Patrick Lopatto, P. M. Aronow
UNC Libraries
Statistical Methods and Inference
article

Nearly-minimax variance estimation under rough random design

Patrick Lopatto, P. M. Aronow
article en

Abstract

We identify the minimax exponent for constant conditional variance estimation under rough random design. The unknown design density is bounded above and away from zero, with no smoothness assumption, and the conditional error laws may depend on the covariates and have uniformly bounded fourth moments. For an $s$-H\"older regression function with $s>1$ in dimension $d>4s$, the minimax root-mean-square risk lies between $cn^{-2(s+1)/(d+4)}e^{-C\sqrt{\log n}}$ and $Cn^{-2(s+1)/(d+4)}$. These bounds show that the rate proposed by Robins is not uniformly attainable over this model class. For $01$ and $d\le4s$, it is $n^{-1/2}$.

UNC Libraries
University of North Carolina at Chapel Hill (US)
Openalex Percentile: Top 8%
Statistical Methods and Inference
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Nearly-minimax variance estimation under rough random design — Patrick Lopatto, P. M. Aronow · UNC Libraries (2026) | TGRS Research Map | TGRS