Selection models are ubiquitous in statistics. In recent years, they have regained considerable popularity as the working inferential models in many selective inference problems. In this paper, we derive an asymptotic expansion of the local likelihood ratios of selection models. We show that under mild regularity conditions, they are asymptotically equivalent to a sequence of Gaussian selection models. This generalizes the Local Asymptotic Normality framework of Le Cam (1960). Furthermore, we derive the asymptotic shape of Bayesian posterior distributions constructed from selection models, and show that they can be significantly miscalibrated in a frequentist sense.

翻译：选择模型在统计学中无处不在。近年来，作为许多选择性推断问题中的工作推断模型，它们重新获得了广泛的关注。本文推导了选择模型局部似然比的渐近展开式。我们证明，在温和的正则条件下，它们渐近等价于一系列高斯选择模型。这推广了Le Cam（1960）的局部渐近正态性框架。此外，我们推导了基于选择模型构建的贝叶斯后验分布的渐近形态，并表明其在频率学派意义下可能存在显著的校准偏差。