Non-Parametric Rank Statistics for Spectral Power and Coherence
Despite advances in multivariate spectral analysis of neural signals, the statistical inference of measures such as spectral power and coherence in practical and real-life scenarios remains a challenge. The non-normal distribution of the neural signals and presence of artefactual components make it difficult to use the parametric methods for robust estimation of measures or to infer the presence of specific spectral components above the chance level. Furthermore, the bias of the coherence measures and their complex statistical distributions are impediments in robust statistical comparisons between 2 different levels of coherence. Non-parametric methods based on the median of auto-/cross-spectra have shown promise for robust estimation of spectral power and coherence estimates. However, the statistical inference based on these non-parametric estimates remain to be formulated and tested. In this report a set of methods based on non-parametric rank statistics for 1-sample and 2-sample testing of spectral power and coherence is provided. The proposed methods were demonstrated and tested using simulated neural signals in different conditions. The results show that non-parametric methods provide robustness against artefactual components. Moreover, they provide new possibilities for robust 1-sample and 2-sample testing of the complex coherency function, including both the magnitude and phase, where existing methods fall short of functionality. The utility of the methods were further demonstrated by examples on experimental neural data. The proposed approach provides a new framework for non-parametric spectral analysis of digital signals. These methods are especially suited to neuroscience and neural engineering applications, given the attractive properties such as minimal assumption on distributions, statistical robustness, and the diverse testing scenarios afforded.