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 parameter with a user-chosen probability, and parameter values different from the true ones will be left out of the confidence region as the number of data points increases. The theoretical results are illustrated in a simulation example.