Testing models for angular power spectra: A distribution-free approach
Sara Algeri, Xiangyu Zhang, Erik Floden, Hongru Zhao, Galin L. Jones, Vuk Mandic, Jesse Miller
TL;DR
This work addresses testing parametric angular power spectrum models when the estimator distribution is unknown. It reframes parameter estimation as a generalized least squares problem and introduces a Khmaladze-2 transformation to produce a limiting, model- and distribution-free null distribution for goodness-of-fit tests, enabling KS-type statistics without case-by-case simulations. The key contribution is a practical, distribution-free testing framework for autocorrelation and cross-correlation angular power spectra, demonstrated via an illustrative example and supported by open-source Python and R implementations. The approach has broad relevance for cosmology and multi-mky sky-map analyses, including anisotropic stochastic gravitational-wave backgrounds and cross-sky map studies, offering computational efficiency and robust inference. The availability of ready-to-use software further facilitates adoption in astrophysical and geophysical applications.
Abstract
A novel goodness-of-fit strategy is introduced for testing models of angular power spectra with unknown parameters. Using this strategy, it is possible to assess the validity of such models without specifying the distribution of the angular power spectrum estimators. This holds under general conditions, ensuring the method's applicability in diverse applications. Moreover, the proposed solution overcomes the need for case-by-case simulations when testing different models, leading to notable computational advantages.