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

12/19/2022

∙

by   Ingvar Ziemann, et al.

∙

0

∙

share

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.