It is demonstrated that estimators of the angular power spectrum commonly used for the stochastic gravitational-wave background (SGWB) lack a closed-form analytical expression for the likelihood function and, typically, cannot be accurately approximated by a Gaussian likelihood. Nevertheless, a robust statistical analysis can be performed to enable the estimation and testing of angular power spectral models for the SGWB without specifying distributional assumptions. Here, the technical aspects of the method are discussed in detail. Moreover, a new, consistent estimator for the covariance of the angular power spectrum is derived. The proposed approach is applied to data from the third observing run (O3) of Advanced LIGO and Advanced Virgo.
@article{arxiv.2504.16959,
title = {On Validating Angular Power Spectral Models for the Stochastic Gravitational-Wave Background Without Distributional Assumptions},
author = {Xiangyu Zhang and Erik Floden and Hongru Zhao and Sara Algeri and Galin Jones and Vuk Mandic and Jesse Miller},
journal= {arXiv preprint arXiv:2504.16959},
year = {2026}
}