@article{b2de83a9e26e44fcb62ad9d08206f4d2,
title = "Monotonicity of the Trace-Inverse of Covariance Submatrices and Two-Sided Prediction",
abstract = "It is common to assess the 'memory strength' of a stationary process by 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). Minimizing this measure is then 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.",
keywords = "Maximum entropy, causality, minimum mean square error, prediction",
author = "Anatoly Khina and Arie Yeredor and Ram Zamir",
note = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",
year = "2022",
month = apr,
day = "1",
doi = "10.1109/TIT.2021.3131912",
language = "אנגלית",
volume = "68",
pages = "2767--2781",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "4",
}