A Generalized Framework for Approximate Co-Sufficient Sampling

TL;DR

This paper extends approximate co-sufficient sampling (aCSS) to include nonlinear regularization and nonparametric estimators, providing a unified, theoretically grounded framework with enhanced flexibility and insights into power optimality.

Contribution

It introduces a generalized aCSS framework that encompasses nonlinear regularization, robust estimators, and unifies existing methods, with rigorous theoretical analysis of validity and power.

Findings

Validates the generalized aCSS framework theoretically.

Characterizes power optimality in high-dimensional settings.

Unifies various conditional sampling methods.

Abstract

Approximate co-sufficient sampling (aCSS) offers a principled route to hypothesis testing when null distributions are unknown, yet current implementations are confined to maximum likelihood estimators with smooth or linear regularization and provide little theoretical insight into power. We present a generalized framework that widens the scope of the aCSS method to embrace nonlinear regularization, such as group lasso and nonconvex penalties, as well as robust and nonparametric estimators. Moreover, we introduce a weighted sampling scheme for enhanced flexibility and propose a generalized aCSS framework that unifies existing conditional sampling methods. Our theoretical analysis rigorously establishes validity and, for the first time, characterizes the power optimality of aCSS procedures in certain high-dimensional settings.