Monotonicity of the Trace-Inverse of Covariance Submatrices and Two-Sided Prediction

Autor:	Khina, Anatoly, Yeredor, Arie, Zamir, Ram
Rok vydání:	2020
Předmět:	Electrical Engineering and Systems Science - Signal Processing Computer Science - Information Theory Electrical Engineering and Systems Science - Systems and Control Mathematics - Statistics Theory
Druh dokumentu:	Working Paper
Popis:	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. Comment: 25 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2011.10810 Zobrazit plný text záznamu View this record from Arxiv