Non-Asymptotic Confidence Sets for the Parameters of Linear Transfer Functions

We consider the problem of constructing confidence sets for the parameters of input-output transfer functions based on observed data. The assumptions on the noise affecting the system are reduced to a minimum; the noise can virtually be anything, but in return the user must be able to select the input signal. In this paper a procedure for solving this problem is developed in the general framework of leave-out sign-dominant confidence regions. The procedure returns confidence regions that are guaranteed to contain the true transfer function with a user-chosen probability for any finite data set.