Finite sample properties of indirect nonparametric closed-loop identification

This paper presents new results on the properties of indirect nonparametric estimation using closed-loop data. Specific results developed include finite sample bias and variance. We show that previous asymptotic results hold only when the signal-to-noise ratio is large. We develop an expression which holds generally and which departs significantly from the known asymptotic results. Simulations are presented which substantiate the validity of the general expression.