Finite sample properties of system identification methods

We study the performance of system identification methods on a finite data sample. Our results are of the following form: with a probability not less than 1-δ, minimising the empirical identification cost leads to an estimate which is within an accuracy ε from the theoretical optimal estimate. Explicit expressions for the accuracy ε are derived, revealing its dependence on the data generation characteristics and the choices made in the system identification procedure. This paper presents a finite sample identification theory applicable to a general linear time-invariant setting