## 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.

Original language | English |
---|---|

Pages (from-to) | 215-220 |

Number of pages | 6 |

Journal | IFAC-PapersOnLine |

Volume | 51 |

Issue number | 15 |

DOIs | |

Publication status | Published - 8 Oct 2018 |

Event | 18th IFAC Symposium on System Identification (SYSID 2018) - Stockholm, Sweden Duration: 9 Jul 2018 → 11 Jul 2018 |

## Keywords

- confidence regions
- distribution-free results
- finite sample results
- input design
- least squares
- parameter estimation
- system identification