Abstract
Finite-sample system identification methods provide statistical inference, typically in the form of confidence regions, with rigorous non-asymptotic guarantees under minimal distributional assumptions. Data Perturbation (DP) methods constitute an important class of such algorithms, which includes, for example, Sign-Perturbed Sums (SPS) as a special case. Here we study a natural input design problem for DP methods in linear regression models, where we want to select the regressors in a way that the expected volume of the resulting confidence regions are minimized. We suggest a general approach to this problem and analyze it for the fundamental building blocks of all DP confidence regions, namely, for ellipsoids having confidence probability exactly 1/2. We also present experiments supporting that minimizing the expected volumes of such ellipsoids significantly reduces the average sizes of the constructed DP confidence regions.
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