Box Confidence Depth: Simulation-based Inference with Hyper-rectangles

• Authors: Elena Bortolato and Laura Ventura
• Electronic Journal of Statistics, Vol. 20, No. 1, 942 - 963, January 2026

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.