Year: 2026
Type: preprint
Abstract: We study the role of design smoothness in the minimax estimation of conditional average treatment effects at a fixed covariate point. For design densities bounded above and away from zero, without further regularity, we derive upper and lower risk bounds with an arbitrarily small gap in the convergence-rate exponent. Under uniform design, we obtain matching upper and lower bounds at interior points in the regime of low nuisance smoothness. These results show that rough covariate designs can lead to slower rates than uniform designs, even under the same smoothness assumptions on the treatment effect and nuisance functions, highlighting the role of the covariate distribution in pointwise causal estimation.
Source: arXiv (Cornell University)
Authors: Hou, Yuxuan, Li, Zhenghan
Institutions: Tsinghua University, University of Minnesota
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221796040