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From Parameter Estimation to Dispersion of Nonstationary Gauss-Markov Processes

Tian, Peida and Kostina, Victoria (2019) From Parameter Estimation to Dispersion of Nonstationary Gauss-Markov Processes. In: 2019 IEEE International Symposium on Information Theory (ISIT). IEEE , Piscataway, NJ, pp. 2044-2048. ISBN 9781538692912. https://resolver.caltech.edu/CaltechAUTHORS:20191004-100332992

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Abstract

This paper provides a precise error analysis for the maximum likelihood estimate â (u) of the parameter a given samples u = (u 1 , … , u n )^⊤ drawn from a nonstationary Gauss-Markov process U i = aU i−1 + Z i , i ≥ 1, where a > 1, U 0 = 0, and Z i ’s are independent Gaussian random variables with zero mean and variance σ^2 . We show a tight nonasymptotic exponentially decaying bound on the tail probability of the estimation error. Unlike previous works, our bound is tight already for a sample size of the order of hundreds. We apply the new estimation bound to find the dispersion for lossy compression of nonstationary Gauss-Markov sources. We show that the dispersion is given by the same integral formula derived in our previous work [1] for the (asymptotically) stationary Gauss-Markov sources, i.e., |a| < 1. New ideas in the nonstationary case include a deeper understanding of the scaling of the maximum eigenvalue of the covariance matrix of the source sequence, and new techniques in the derivation of our estimation error bound.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/isit.2019.8849797DOIArticle
https://arxiv.org/abs/1907.00304arXivDiscussion Paper
ORCID:
AuthorORCID
Tian, Peida0000-0003-3665-8173
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2019 IEEE. This research was supported in part by the National Science Foundation (NSF) under Grant CCF-1751356.
Funders:
Funding AgencyGrant Number
NSFCCF-1751356
Subject Keywords:Parameter estimation, maximum likelihood estimator, unstable processes, finite blocklength analysis, lossy compression, sources with memory, rate-distortion theory, covering in stochastic processes
Record Number:CaltechAUTHORS:20191004-100332992
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191004-100332992
Official Citation:P. Tian and V. Kostina, "From Parameter Estimation to Dispersion of Nonstationary Gauss-Markov Processes," 2019 IEEE International Symposium on Information Theory (ISIT), Paris, France, 2019, pp. 2044-2048. doi: 10.1109/ISIT.2019.8849797
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99076
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:04 Oct 2019 18:24
Last Modified:04 Oct 2019 18:24

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