Box Confidence Depth: simulation-based inference with hyper-rectangles

TL;DR

This paper introduces a simulation-based method using hyper-rectangles and data depth to construct confidence regions for parameters in complex models, especially when traditional methods are unreliable due to limited data or non-standard conditions.

Contribution

It proposes a novel approach that creates hyper-rectangle confidence regions via simulation, applicable to multivariate parameters and test statistics, improving inference in challenging scenarios.

Findings

Effective in small-sample and complex models

Provides calibrated confidence sets from simulation

Addresses multivariate parameter inference

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.