On robustness of Spectral Rényi divergence

Abstract

This paper studies a specific class of statistical divergences for spectral densities of time series: the spectral $α$-Rényi divergences, which include the Itakura-Saito divergence as a limiting case. The aim of this paper is to highlight both information-theoretic and statistical properties of spectral $α$-Rényi divergences. We reveal the connection between the spectral $α$-Rényi divergence and the $γ$-divergence in robust statistics, and a variational representation of the spectral $α$-Rényi divergence. Inspired by these results suggesting "robustness" of spectral