In statistical inference, it is rarely realistic that the hypothesized statistical model is well-specified, and 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 of Wasserman et al. (2020) and is based on inverting a family of split-sample tests of relative fit. We study settings in which our methods yield either exact or approximate, finite-sample valid confidence sets for various projection distributions. We study rates at which the resulting confidence sets shrink around the target of inference and complement these results with a simulation study.

翻译：在统计推断中，假设的统计模型完全正确这一情形在现实中极少成立，因此理解模型误设对推断过程的影响至关重要。当假设的统计模型存在误设时，推断的自然目标是数据生成分布向模型的投影。我们提出了一种通用方法，用于在弱正则条件下为这类投影构造有效的置信集，即使模型可能存在误设。该方法基于Wasserman等人(2020)提出的通用推断方法，并通过对一系列相对拟合度的分裂样本检验进行逆变换来实现。我们研究了在何种条件下，该方法能为各类投影分布提供精确或近似有效的有限样本置信集。同时，我们分析了所得置信集围绕推断目标收缩的速率，并通过模拟研究对这些理论结果进行了补充验证。