Sign-Perturbed Sums (SPS) is a system identification method that constructs non-asymptotic confidence regions for the parameters of linear regression models under mild statistical assumptions. One of its main features is that, for any finite number of data points and any user-specified probability, the constructed confidence region contains the true system parameter with exactly the user-chosen probability. In this paper we examine the size and the shape of the confidence regions, and we show that the regions are strongly consistent, i.e., they almost surely shrink around the true parameter as the number of data points increases. Furthermore, the confidence region is contained in a marginally inflated version of the confidence ellipsoid obtained from the asymptotic system identification theory. The results are also illustrated by a simulation example.
Asymptotic properties of SPS confidence regions
Weyer E.;Campi M. C.
;Csaji B. C.
2017-01-01
Abstract
Sign-Perturbed Sums (SPS) is a system identification method that constructs non-asymptotic confidence regions for the parameters of linear regression models under mild statistical assumptions. One of its main features is that, for any finite number of data points and any user-specified probability, the constructed confidence region contains the true system parameter with exactly the user-chosen probability. In this paper we examine the size and the shape of the confidence regions, and we show that the regions are strongly consistent, i.e., they almost surely shrink around the true parameter as the number of data points increases. Furthermore, the confidence region is contained in a marginally inflated version of the confidence ellipsoid obtained from the asymptotic system identification theory. The results are also illustrated by a simulation example.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
