论文标题
协方差一量和双向预测的痕量截留性的单调性
Monotonicity of the Trace-Inverse of Covariance Submatrices and Two-Sided Prediction
论文作者
论文摘要
通常，评估固定过程的“记忆强度”，以了解其协方差的标准化对数确定因素的速度（即熵率）降低。在这项工作中，我们提出了一种替代表征，以协方差的标准化痕量侵略。我们表明，当且仅当过程是白色时，此序列在单调上是非降低的，并且是恒定的。此外，虽然熵率与单方面的预测错误相关联（从过去出现），但新措施与双面预测错误（从过去和未来出现）相关联。该度量可以用作Burg的最大渗透原理的替代方法，以进行光谱估计。我们还通过查看子集的平均痕量截距，为非平稳过程提出了一个对应物。
It is common to assess the "memory strength" of a stationary process looking at how fast the normalized log-determinant of its covariance submatrices (i.e., entropy rate) decreases. In this work, we propose an alternative characterization in terms of the normalized trace-inverse of the covariance submatrices. We show that this sequence is monotonically non-decreasing and is constant if and only if the process is white. Furthermore, while the entropy rate is associated with one-sided prediction errors (present from past), the new measure is associated with two-sided prediction errors (present from past and future). This measure can be used as an alternative to Burg's maximum-entropy principle for spectral estimation. We also propose a counterpart for non-stationary processes, by looking at the average trace-inverse of subsets.
