ON THE CHOICE OF NORMS IN SYSTEM-IDENTIFICATION

In this paper we discuss smooth and sensitive norms for prediction err or system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitud e faster convergence of the parameter estimate variance, are developed . However, it also is shown that the parameter estimate variance conve rgence rate of sensitive norms is arbitrarily bad for certain distribu tions. A necessary condition for a norm to be statistically robust wit h respect to the family F(C) of distributions with support [-C,C] for some arbitrary C > 0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quad ratic norm is statistically robust among all l(p)-norms, p less than o r equal to 2 < infinity for F(C).