Subspace identification is claimed to have O(1/sqrt N) finite-sample matrix errors, O(N^{-1/(2n)}) pole errors, and a super-polynomial sample complexity in n/m; the last claim is not proven.
Verhaegen, Identification of the deterministic part of mimo state space models given in innovations form from input-output data, Automatica 30 (1) (1994) 61–74
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Finite Sample Analysis of Subspace Identification for Stochastic Systems
Subspace identification is claimed to have O(1/sqrt N) finite-sample matrix errors, O(N^{-1/(2n)}) pole errors, and a super-polynomial sample complexity in n/m; the last claim is not proven.