Confidence intervals for tree-structured varying coefficients
针对树结构变系数模型，提出了一种基于参数自助法的置信区间构建方法，用于量化估计系数的不确定性，并通过模拟和医疗数据验证了其有效性。
The tree-structured varying coefficient (TSVC) model is a flexible regression approach that allows the effects of covariates to vary with the values of the effect modifiers. Relevant effect modifiers are identified inherently using recursive partitioning techniques. To quantify uncertainty in TSVC models, a procedure to construct confidence intervals of the estimated partition-specific coefficients is proposed. This task constitutes a selective inference problem as the coefficients of a TSVC model result from data-driven model building. To account for this issue, a parametric bootstrap approach, which is tailored to the complex structure of TSVC, is introduced. Finite sample properties, particularly coverage proportions, of the proposed confidence intervals are evaluated in a simulation study. For illustration, applications to data from COVID-19 patients and from patients suffering from acute odontogenic infection are considered. The proposed approach may also be adapted for constructing confidence intervals for other tree-based methods.