A note on the smallest eigenvalue of the empirical covariance of causal Gaussian processes

• URL: http://arxiv.org/abs/2212.09508v2
• Date: Fri, 27 Oct 2023 22:48:58 GMT
• Title: A note on the smallest eigenvalue of the empirical covariance of causal Gaussian processes
• Authors: Ingvar Ziemann
• Abstract summary: We present a proof for bounding the smallest eigenvalue of the empirical covariance in a causal Gaussian process. We establish a one-sided tail inequality for Gaussian quadratic forms using a causal decomposition.
• Score: 1.223779595809275
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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