Shapley Curves: A Smoothing Perspective
从非参数平滑视角研究夏普利值作为变量重要性度量的统计性质，定义总体夏普利曲线，推导估计量的收敛速度和渐近正态性，并针对有限样本提出改进的bootstrap方法。
This article fills the limited statistical understanding of Shapley values as a variable importance measure from a nonparametric (or smoothing) perspective. We introduce population-level <i>Shapley curves</i> to measure the true variable importance, determined by the conditional expectation function and the distribution of covariates. Having defined the estimand, we derive minimax convergence rates and asymptotic normality under general conditions for the two leading estimation strategies. For finite sample inference, we propose a novel version of the wild bootstrap procedure tailored for capturing lower-order terms in the estimation of Shapley curves. Numerical studies confirm our theoretical findings, and an empirical application analyzes the determining factors of vehicle prices.