论文标题
关于因果高斯过程的经验协方差的最小特征值的注释
A note on the smallest eigenvalue of the empirical covariance of causal Gaussian processes
论文作者
论文摘要
我们提供了一个简单的证据，用于在因果高斯过程中界定经验协方差的最小特征值。一路上，我们使用因果分解为高斯二次形式建立了单方面的尾巴不等式。我们的证明只使用有关高斯分布和联合界限的基本事实。我们以一个例子为例，在该示例中，我们为矢量自动降低的最小二乘识别提供了性能保证。
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.
