TY - JOUR
T1 - Towards D-optimal input design for finite-sample system identification
AU - Kolumbán, Sándor
AU - Csáji, Balázs Csanád
PY - 2018/10/8
Y1 - 2018/10/8
N2 - 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.
AB - 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.
KW - confidence regions
KW - distribution-free results
KW - finite sample results
KW - input design
KW - least squares
KW - parameter estimation
KW - system identification
UR - http://www.scopus.com/inward/record.url?scp=85054379725&partnerID=8YFLogxK
U2 - 10.1016/j.ifacol.2018.09.136
DO - 10.1016/j.ifacol.2018.09.136
M3 - Conference article
AN - SCOPUS:85054379725
SN - 2405-8963
VL - 51
SP - 215
EP - 220
JO - IFAC-PapersOnLine
JF - IFAC-PapersOnLine
IS - 15
T2 - 18th IFAC Symposium on System Identification (SYSID 2018)
Y2 - 9 July 2018 through 11 July 2018
ER -