Abstract
The purpose of this paper is first to derive the expressions of the Chernoff, Bhattacharyya, Rényi and Sharma-Mittal divergences when comparing two probability density functions of vectors storing k consecutive samples of Gaussian ARMA processes. This can be useful for process comparison or statistical change detection issue. Then, we analyze the behaviors of the divergences when k increases and tends to infinity by using some results related to ARMA processes such as the Yule-Walker equations. Comments and illustrations are given.
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Notes
- 1.
The definition of \(Q_{k,\alpha }\) amounts to saying that a third process is introduced and corresponds to a linear combination of the two processes to be compared.
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Grivel, E. (2021). Chernoff, Bhattacharyya, Rényi and Sharma-Mittal Divergence Analysis for Gaussian Stationary ARMA Processes. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham. https://doi.org/10.1007/978-3-030-80209-7_53
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DOI: https://doi.org/10.1007/978-3-030-80209-7_53
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