This work presents a novel simulation-based approach for constructing confidence regions in parametric models, which is particularly suited for generative models and situations where limited data and conventional asymptotic approximations fail to provide accurate results. The method leverages the concept of data depth and depends on creating random hyper-rectangles, i.e. boxes, in the sample space generated through simulations from the model, varying the input parameters. A probabilistic acceptance rule allows to retrieve a Depth-Confidence Distribution for the model parameters from which point estimators as well as calibrated confidence sets can be read-off. The method is designed to address cases where both the parameters and test statistics are multivariate.

翻译：本研究提出了一种新颖的基于模拟的参数模型置信区域构建方法，该方法特别适用于生成模型以及有限数据和传统渐近近似无法提供准确结果的情况。该方法利用数据深度的概念，通过在模型参数变化时从模型模拟生成的样本空间中创建随机超矩形（即盒子）来实现。基于概率接受准则，可以从模型参数中提取深度-置信分布，进而获得点估计量以及经过校准的置信集。该方法旨在解决参数与检验统计量均为多元变量的情形。