A Note on the Smallest Eigenvalue of the Empirical Covariance of Causal Gaussian Processes

• 成果类型: Article
• 署名作者: Ziemann, Ingvar
• 署名单位: University of Pennsylvania
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3326061
• 发表日期: 2024
• 页码: 1372-1376
• 关键词: probability; System identification

摘要

We present a simple proof for bounding the smallest eigenvalue of the empirical covariance in a causal Gaussian process. Along the way, we establish a one-sided tail inequality for Gaussian quadratic forms using a causal decomposition. Our proof only uses elementary facts about the Gaussian distribution and the union bound. We conclude with an example in which we provide a performance guarantee for least squares identification of a vector autoregression.