TY - JOUR
T1 - Robust Parametric Identification for ARMAX Models with Non-Gaussian and Coloured Noise
T2 - A Survey
AU - Escobar, Jesica
AU - Poznyak, Alexander
N1 - Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2022/4/1
Y1 - 2022/4/1
N2 - In this paper the Cramer-Rao information bound for ARMAX (Auto-Regression-Moving-Average-Models-with-Exogenuos-inputs) under non-Gaussian noise is derived. It is shown that the direct application of the Least Squares Method (LSM) leads to incorrect (shifted) parameter estimates. This inconsistency can be corrected by the implementation of the parallel usage of the MLMW (Maximum Likelihood Method with Whitening) procedure, applied to all measurable variables of the model, and a nonlinear residual transformation using the information on the distribution density of a non-Gaussian noise, participating in Moving Average structure. The design of the corresponding parameter-estimator, realizing the suggested MLMW-procedure is discussed in details. It is shown that this method is asymptotically optimal, that is, reaches this information bound. If the noise distribution belongs to some given class, then the Huber approach (min-max version of MLM) may be effectively applied. A numerical example illustrates the suggested approach.
AB - In this paper the Cramer-Rao information bound for ARMAX (Auto-Regression-Moving-Average-Models-with-Exogenuos-inputs) under non-Gaussian noise is derived. It is shown that the direct application of the Least Squares Method (LSM) leads to incorrect (shifted) parameter estimates. This inconsistency can be corrected by the implementation of the parallel usage of the MLMW (Maximum Likelihood Method with Whitening) procedure, applied to all measurable variables of the model, and a nonlinear residual transformation using the information on the distribution density of a non-Gaussian noise, participating in Moving Average structure. The design of the corresponding parameter-estimator, realizing the suggested MLMW-procedure is discussed in details. It is shown that this method is asymptotically optimal, that is, reaches this information bound. If the noise distribution belongs to some given class, then the Huber approach (min-max version of MLM) may be effectively applied. A numerical example illustrates the suggested approach.
KW - Fisher information
KW - least squares method
KW - maximum likelihood method
KW - nonlinear residual transformation
KW - parameter estimation
KW - whitening filter
UR - http://www.scopus.com/inward/record.url?scp=85128991028&partnerID=8YFLogxK
U2 - 10.3390/math10081291
DO - 10.3390/math10081291
M3 - Artículo
AN - SCOPUS:85128991028
SN - 2227-7390
VL - 10
JO - Mathematics
JF - Mathematics
IS - 8
M1 - 1291
ER -