English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study the estimation problem for linear time-invariant (LTI) state-spacemodels with Gaussian excitation of an unknown covariance. We provide nonasymptotic lower bounds for the expected estimation error and the mean squareestimation risk of the least square estimator, and the minimax mean squareestimation risk. These bounds are sharp with explicit constants when the matrixof the dynamics has no eigenvalues on the unit circle and are rate-optimal whenthey do. Our results extend and improve existing lower bounds to lower boundsin expectation of the mean square estimation risk and to systems with a generalnoise covariance. Instrumental to our derivation are new concentration resultsfor rescaled sample covariances and deviation results for the correspondingmultiplication processes of the covariates, a differential geometricconstruction of a prior on the unit operator ball of small Fisher information,and an extension of the Cram\'er-Rao and van Treesinequalities to matrix-valuedestimators.

Non asymptotic estimation lower bounds for LTI state space models with Cram\'er-Rao and van Trees