TY - GEN
T1 - Dealing with collinearity in FIR models using multiscale estimation
AU - Nounou, Mohamed N.
PY - 2005
Y1 - 2005
N2 - In this paper, multiscale representation of data is utilized to reduce the collinearity problem often encountered in Finite Impulse Response (FIR) modeling. The idea is to decompose the input-output data at multiple scales, use the scaled signal approximations of the data to construct a FIR model at each scale, and then select among all scales the optimum estimated FIR model. The rationale behind this approach is that the number of significant cross correlation function (CCF) coefficients estimated using the scaled signal approximations of the input-output data decreases at coarser scales. This means that more parsimonious FIR models, with less collinearity and improved estimation accuracy, can be constructed at coarser scales. Of course, the estimation accuracy will deteriorate at very coarse scales. Therefore, it is very important to select the most appropriate scale for modeling purposes, which can be done by selecting the scale which results in the maximum prediction signal to noise ratio. The developed multiscale FIR modeling approach is shown to outperform existing methods, such as ordinary least squares (OLS) regression and ridge regression (RR).
AB - In this paper, multiscale representation of data is utilized to reduce the collinearity problem often encountered in Finite Impulse Response (FIR) modeling. The idea is to decompose the input-output data at multiple scales, use the scaled signal approximations of the data to construct a FIR model at each scale, and then select among all scales the optimum estimated FIR model. The rationale behind this approach is that the number of significant cross correlation function (CCF) coefficients estimated using the scaled signal approximations of the input-output data decreases at coarser scales. This means that more parsimonious FIR models, with less collinearity and improved estimation accuracy, can be constructed at coarser scales. Of course, the estimation accuracy will deteriorate at very coarse scales. Therefore, it is very important to select the most appropriate scale for modeling purposes, which can be done by selecting the scale which results in the maximum prediction signal to noise ratio. The developed multiscale FIR modeling approach is shown to outperform existing methods, such as ordinary least squares (OLS) regression and ridge regression (RR).
UR - http://www.scopus.com/inward/record.url?scp=33847204697&partnerID=8YFLogxK
U2 - 10.1109/CDC.2005.1583483
DO - 10.1109/CDC.2005.1583483
M3 - Conference contribution
AN - SCOPUS:33847204697
SN - 0780395689
SN - 9780780395688
T3 - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
SP - 8162
EP - 8167
BT - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
T2 - 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Y2 - 12 December 2005 through 15 December 2005
ER -