Box Confidence Depth: Simulation-Based Inference with Hyper-Rectangles

Laura Ventura and Elena Bortolato

No 1518, Working Papers from Barcelona School of Economics

Abstract: 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.

Keywords: Confidence regions; depth functions; Monte Carlo methods; order statistics; simulation-based methods (search for similar items in EconPapers)
JEL-codes: C12 C13 C15 (search for similar items in EconPapers)
Date: 2025-10
New Economics Papers: this item is included in nep-ecm
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