Non-asymptotic confidence regions for the parameters of EIV systems

Abstract

In this paper we consider the problem of constructing non-asymptotic confidence regions for the parameters of Errors-In-Variables (EIV) systems where both inputs and outputs are observed in noise. The Leave-out Sign-dominant Correlation Regions (LSCR) and Sign-Perturbed Sums (SPS) approaches which are two methods for constructing confidence regions from a finite number of data points, are extended to EIV systems. An appropriate correlation sequence which is required for both LSCR and SPS, is computed by a Kalman filter, and accordingly, a state-space form of the EIV system where both input and output are regarded as outputs is utilized. The constructed confidence regions include the true par..