Mohamad Kazem Shirani Faradonbeh, Ambuj Tewari, George Michailidis
arXiv 5 Oct 2017 · cs.SY · publishedAutomatica (2018) · 98 citations (OpenAlex)
arXiv:1710.01852 · PDF · DOI · OpenAlex · Extracted main text
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially regarding finite time bounds. For this setting, classical results on least-squares estimation of the dynamics parameters are not applicable and therefore new concepts and technical approaches need to be developed to address the issue. Unstable linear systems arise in key real applications in control theory, econometrics, and finance. This study establishes finite time bounds for the identification error of the least-squares estimates for a fairly large class of heavy-tailed noise distributions, and transition matrices of such systems. The results relate the time length (samples) required for estimation to a function of the problem dimension and key characteristics of the true underlying transition matrix and the noise distribution. To establish them, appropriate concentration inequalities for random matrices and for sequences of martingale differences are leveraged.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | D. P. Bertsekas, Dynamic programming and optimal control. 1em plus 0… (1995) vol. 1, no. 2 | 0.811 | 4 | 2 | 100% |
| 2 | T. Söderström, Discrete-time stochastic systems: estimation and cont… (2012) | 0.811 | 4 | 2 | 100% |
| 3 | J. A. Tropp, “User-friendly tail bounds for sums of random matrices,… (2012) User-friendly tail bounds for sums of random matrices | 0.737 | 5 | 4 | 40% |
| 4 | Y. Abbasi-Yadkori, D. Pál, and C. Szepesvári, “Online least squares… (2011) Online least squares estimation with self-normalized processes: An application to bandit problems | 0.737 | 3 | 2 | 100% |
| 5 | T. Engsted, “Explosive bubbles in the cointegrated var model,” Finan… (2006) Explosive bubbles in the cointegrated var model | 0.737 | 3 | 2 | 100% |
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| 8 | T. Lai and C. Wei, “Asymptotic properties of general autoregressive… (1983) Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters | 0.644 | 2 | 2 | 100% |
| 9 | B. Nielsen, “Strong consistency results for least squares estimators… (2009) Singular vector autoregressions with deterministic terms: Strong consistency and lag order determination | 0.644 | 2 | 2 | 100% |
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Showing the top 10 of 44 scored citations.