Formal theory for higher-moment matching effects in wild bootstrap performance

Develop a formal theoretical framework quantifying how matching higher moments (beyond the third) in wild bootstrap weights affects coverage accuracy and distributional approximation for high-dimensional maxima (e.g., T_n and ∥S_n∥_∞), particularly to explain the strong empirical performance of the Rademacher wild bootstrap in symmetric settings.

Background

The simulation paper observes that Rademacher wild bootstrap performs remarkably well in symmetric cases, and the authors suggest higher-moment matching as a possible explanation but note the lack of formal theory.

A rigorous treatment would clarify the role of higher moments in bootstrap accuracy for maximum-type statistics and potentially guide the design of improved bootstrap procedures.