Testing Rank of Incomplete Unimodal Matrices

TL;DR

This paper introduces a new variance ratio statistic for source detection in incomplete unimodal matrices, demonstrating improved performance over existing methods through theoretical analysis and numerical experiments.

Contribution

A novel variance ratio statistic for source detection in unimodal matrices, with asymptotic analysis and optimized rotations for enhanced accuracy.

Findings

Variance ratio detector outperforms existing methods

Optimal rotations further improve detection accuracy

Numerical experiments confirm performance gains

Abstract

Several statistics-based detectors, based on unimodal matrix models, for determining the number of sources in a field are designed. A new variance ratio statistic is proposed, and its asymptotic distribution is analyzed. The variance ratio detector is shown to outperform the alternatives. It is shown that further improvements are achievable via optimally selected rotations. Numerical experiments demonstrate the performance gains of our detection methods over the baseline approach.