2017/06/02 by Xiaowu Dai, Peter Chien, Dai, Xiaowu +1
Decision Sciences · Mathematics · #62G05 #62G08 #62H12 (Primary) #62P20 (Secondary) #FOS: Mathematics #Probabilistic and Robust Engineering Design #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1706.00850
openalex publication_date 2017/06/02 · openalex created_date 2018/01/05 · openalex updated_date 2026/07/28
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 derivatives. For additive models, the rates by using all first-order partial derivatives are root-n to achieve the "parametric rate". We also investigate the minimax optimal rates for first-order partial derivative estimations when derivative data are available. Those rates coincide with the optimal rate for estimating the first-order derivative of a univariate function.