Minimax Optimal Procedures for Joint Detection and Estimation

2026-04-24

AI Summary

This study addresses the joint problem of composite hypothesis testing and random parameter estimation under distributional uncertainty by establishing a unified minimax optimization framework. Optimal strategies are derived under both Bayesian and Neyman–Pearson–type statistical criteria. The key innovation lies in uncovering an intrinsic connection between the optimal detection–estimation architecture and f-similarity, enabling the identification of least favorable distributions through maximization of f-similarity. Robust design is achieved by integrating this insight with a band-shaped uncertainty model. The proposed approach enhances existing numerical algorithms, offering improved stability while preserving convergence guarantees. Experimental results demonstrate the superiority of the framework in terms of both performance and robustness.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

We investigate the problem of jointly testing a pair of composite hypotheses and, depending on the test result, estimating a random parameter under distributional uncertainties. Specifically, it is assumed that the distribution of the data given the parameter of interest, is subject to uncertainty. Both, a Bayesian formulation and a Neyman-Pearson-like formulation, are considered. It is shown that the optimal policy induces an $f$-similarity that must be maximized to identify the least favorable distributions. Besides the general results, the implementation is investigated using a band-type uncertainty model. For designing the minimax procedures, existing algorithms are modified to increase convergence speed while maintaining numerical stability. The proposed theory is supplemented by numerical results for both formulations.

Problem

• joint detection and estimation
• distributional uncertainty
• minimax optimality
• composite hypotheses
• random parameter estimation

Innovation

• minimax optimization
• joint detection and estimation
• distributional uncertainty
• f-similarity
• least favorable distributions