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的情况极为罕见，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，推断的自然目标是将数据生成分布投影到模型上的结果。我们提出了一种通用方法，用于为此类投影构建有效的置信集，该方法在较弱的正则性条件下仍能保证有效性，且不受模型可能存在的误设影响。我们的方法建立在Wasserman等人（2020）提出的通用推断方法基础上，通过反转一系列基于数据分割的相对拟合检验来实现。我们研究了在不同设定下，该方法如何为各类投影分布生成精确或近似、且具有有限样本有效性的置信集。我们分析了所得置信集围绕推断目标的收缩速率，并通过模拟研究对这些结果进行了补充验证。