Estimation and Hypothesis Testing of Derivatives in Smoothing Spline ANOVA Models

Understand

Within the framework of smoothing spline ANOVA, we propose a plug-in kernel ridge regression estimator to estimate the derivatives of the underlying multivariate regression function.

• We first establish an $L_\infty$ convergence rate of the proposed estimator under general random designs.
• When the covariates are uniformly distributed, we provide a in-depth analysis that includes a sharp upper bound and the minimax lower bound of the $L_2$ convergence rate.
• Additionally, motivated by a wide range of applications, we propose a hypothesis testing procedure to examine whether a derivative is zero.