多变量谱密度的距离与黎曼度量
Distances and Riemannian metrics for multivariate spectral densities
AI总结：
本文引入功率谱密度矩阵间的散度度量，通过最优预测比较模型，导出黎曼度量并给出测地线与距离的显式公式，揭示了与Fisher-Rao度量的联系。
摘要：
我们首先引入功率谱密度矩阵之间的一类散度度量。这些度量是通过在最优预测背景下比较不同模型的适用性而推导出来的。“无穷小接近”的功率谱之间的距离是二次的，因此它们诱导出微分几何结构。我们研究了相应的黎曼度量，并在特定情况下给出了相应的测地线和测地距离的显式公式。注意到功率谱的几何与Fisher-Rao度量的几何之间的密切联系。
英文摘要：
We first introduce a class of divergence measures between power spectral density matrices. These are derived by comparing the suitability of different models in the context of optimal prediction. Distances between "infinitesimally close" power spectra are quadratic, and hence, they induce a differential-geometric structure. We study the corresponding Riemannian metrics and, for a particular case, provide explicit formulae for the corresponding geodesics and geodesic distances. The close connection between the geometry of power spectra and the geometry of the Fisher-Rao metric is noted.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
