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Non asymptotic estimation lower bounds forLTI state space models with Cramér-Rao and van Trees
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- Djehiche, Boualem, 1962- (author)
- KTH,Matematisk statistik
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- Mazhar, Othmane, Ph.D. student, 1990- (author)
- KTH,Matematisk statistik
- (creator_code:org_t)
- English.
- Other publication (other academic/artistic)
Abstract
Subject headings
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- We study the estimation problem for linear time-invariant (LTI) state-space models with Gaussian excitation of an unknown covariance. We provide non asymptotic lower bounds for the expected estimation error and the mean square estimation risk of the least square estimator, and the minimax mean square estimation risk. These bounds are sharp with explicit constants when the matrix of the dynamics has no eigenvalues on the unit circle and are rate-optimal when they do. Our results extend and improve existing lower bounds to lower bounds in expectation of the mean square estimation risk and to systems with a general noise covariance. Instrumental to our derivation are new concentration results for rescaled sample covariances and deviation results for the corresponding multiplication processes of the covariates, a differential geometric construction of a prior on the unit operator ball of small Fisher information, and an extension of the Cramér-Rao and van Treesinequalities to matrix-valued estimators.
Subject headings
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Keyword
- linear time invariant state space models
- least squares
- on asymptotic estimation
- minimax risk
- samplecomplexity
- sample covariance
- multiplication process
- concentration inequality
- Cramér-Rao
- van Trees inequal-ity
- Fisher information
- Matematisk statistik
- Mathematical Statistics
Publication and Content Type
- vet (subject category)
- ovr (subject category)
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