Towards D-optimal input design for finite-sample system identification
| Autor: | Balázs Csanád Csáji, Sándor Kolumbán |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
0209 industrial biotechnology
confidence regions Estimation theory System identification Perturbation (astronomy) input design 020206 networking & telecommunications 02 engineering and technology Ellipsoid least squares 020901 industrial engineering & automation Input design finite sample results Control and Systems Engineering distribution-free results Linear regression 0202 electrical engineering electronic engineering information engineering Statistical inference Special case parameter estimation Algorithm Mathematics system identification |
| Zdroj: | IFAC-PapersOnLine. 51(15):215-220 |
| ISSN: | 2405-8963 |
| DOI: | 10.1016/j.ifacol.2018.09.136 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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