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Minimax rates for pointwise CATE estimation: the role of design smoothness
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.
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BibTeX
@misc{hou2026minimax,
title = {{Minimax rates for pointwise CATE estimation: the role of design smoothness}},
author = {Yuxuan Hou and Zhenghan Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18623},
eprint = {2610.18623},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18623},
}
RIS
TY - UNPB
TI - Minimax rates for pointwise CATE estimation: the role of design smoothness
AU - Yuxuan Hou
AU - Zhenghan Li
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18623
UR - https://arxiv.org/abs/2610.18623
AB - 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.
ER -