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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.06902 |
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| _version_ | 1866913049048252416 |
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| author | Takabatake, Tetsuya Yano, Keisuke |
| author_facet | Takabatake, Tetsuya Yano, Keisuke |
| contents | 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 $α$-Rényi divergence, we show that the minimum spectral Rényi divergence estimate has a stable optimization path with respect to outliers in the frequency domain, unlike the minimum Itakura-Saito divergence estimator, and thus it delivers more stable estimates, reducing the need for intricate pre-processing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06902 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On robustness of Spectral Rényi divergence Takabatake, Tetsuya Yano, Keisuke Statistics Theory 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 $α$-Rényi divergence, we show that the minimum spectral Rényi divergence estimate has a stable optimization path with respect to outliers in the frequency domain, unlike the minimum Itakura-Saito divergence estimator, and thus it delivers more stable estimates, reducing the need for intricate pre-processing. |
| title | On robustness of Spectral Rényi divergence |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2310.06902 |