# Minimax Optimal Rates of Estimation in Functional ANOVA Models with Derivatives

@article{Dai2017MinimaxOR, title={Minimax Optimal Rates of Estimation in Functional ANOVA Models with Derivatives}, author={Xiaowu Dai and Peter Chien}, journal={arXiv: Statistics Theory}, year={2017} }

We establish minimax optimal rates of convergence for nonparametric estimation in functional ANOVA models when data from first-order partial derivatives are available. Our results reveal that partial derivatives can improve convergence rates for function estimation with deterministic or random designs. In particular, for full $d$-interaction models, the optimal rates with first-order partial derivatives on $p$ covariates are identical to those for $(d-p)$-interaction models without partial…

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