Towards a robust frequency-domain analysis: Spectral Rényi divergence revisited

This paper studies a specific category of statistical divergences for spectral densities of time series: the spectral $\alpha$-R\'{e}nyi divergences, which includes the Itakura-Saito divergence as a subset. While the spectral R\'{e}nyi divergence has been acknowledged in past works, its statistical attributes have not been thoroughly investigated. The aim of this paper is to highlight these properties. We reveal a variational representation of spectral R\'{e}nyi divergence, from which the minimum spectral R\'{e}nyi divergence estimator is shown to be robust against outliers in the frequency domain, unlike the minimum Itakura-Saito divergence estimator, and thus it delivers more stable estimate, reducing the need for intricate pre-processing.