Efficient estimation of measures of functional dependence
Abstract
Measures of functional dependence that characterize both independence and perfect dependence have attracted growing interest. Despite their appealing theoretical properties, existing rank- and graph-based estimators can suffer from substantial bias under general dependence, limiting their usefulness for statistical inference. Moreover, a systematic and practically accessible framework for mitigating such bias while achieving semiparametric efficiency remains largely unavailable. In this paper, we develop a general framework for efficient estimation of measures of functional dependence through sample-splitting and cross-fitting. Our approach enables systematic bias reduction and semiparametrically efficient inference, and thus offers a flexible and theoretically grounded alternative to existing rank- and graph-based methods.
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BibTeX
@misc{dette2026efficient,
title = {{Efficient estimation of measures of functional dependence}},
author = {Holger Dette and Fang Han},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25421},
eprint = {2610.25421},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25421},
}
RIS
TY - UNPB
TI - Efficient estimation of measures of functional dependence
AU - Holger Dette
AU - Fang Han
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25421
UR - https://arxiv.org/abs/2610.25421
AB - Measures of functional dependence that characterize both independence and perfect dependence have attracted growing interest. Despite their appealing theoretical properties, existing rank- and graph-based estimators can suffer from substantial bias under general dependence, limiting their usefulness for statistical inference. Moreover, a systematic and practically accessible framework for mitigating such bias while achieving semiparametric efficiency remains largely unavailable. In this paper, we develop a general framework for efficient estimation of measures of functional dependence through sample-splitting and cross-fitting. Our approach enables systematic bias reduction and semiparametrically efficient inference, and thus offers a flexible and theoretically grounded alternative to existing rank- and graph-based methods.
ER -