Robust universal inference for misspecified models
提出一种在模型可能误设定时仍能构建有效置信集的通用方法，基于分割样本的相对拟合检验，适用于投影分布，并通过模拟和因果发现案例验证。
Summary In statistical inference, it is rarely realistic to assume that the hypothesized statistical model is well specified; consequently, it is important to understand the effects of misspecification on inferential procedures. When the hypothesized statistical model is misspecified, the natural target of inference is a projection of the data-generating distribution onto the model. We present a general method for constructing valid confidence sets for such projections, under weak regularity conditions, despite possible model misspecification. Our method builds upon the universal inference method and is based on inverting a family of split-sample tests of relative fit. We study settings in which our method yields either exact or approximate, finite-sample valid confidence sets for various projection distributions. We examine the rates at which the resulting confidence sets shrink around their target of inference and complement these results with a simulation study and a study of causal discovery using a linear causal model with the CausalEffectPairs dataset.