Guaranteed Non-Asymptotic Confidence Ellipsoids for FIR Systems

Weyer, Erik and Csáji, Balázs Csanád and Campi, Marco (2013) Guaranteed Non-Asymptotic Confidence Ellipsoids for FIR Systems. In: 52nd IEEE Conference on Decision and Control (CDC), December 10-13, 2013, Florence, Italy.

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Abstract

Recently, a new finite-sample system identification algorithm, called Sign-Perturbed Sums (SPS), was introduced in [2]. SPS constructs finite-sample confidence regions that are centered around the least squares estimate, and are guaranteed to contain the true system parameters with a user-chosen exact probability for any finite number of data points. The main assumption of SPS is that the noise terms are independent and symmetrically distributed about zero, but they do not have to be stationary, nor do their variances and distributions have to be known. Although it is easy to determine if a particular parameter belongs to the confidence region, it is not easy to describe the boundary of the region, and hence to compactly represent the exact confidence region. In this paper we show that an ellipsoidal outer-approximation of the SPS confidence region can be found by solving a convex optimization problem, and we illustrate the properties of the SPS region and the ellipsoidal outer-approximation in simulation examples.

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