TY - GEN

T1 - A modified EM algorithm for parameter estimation in linear models with time-dependent autoregressive and t-distributed errors

AU - Kargoll, Boris

AU - Omidalizarandi, Mohammad

AU - Alkhatib, Hamza

AU - Schuh, Wolf-Dieter

PY - 2017

Y1 - 2017

N2 - We derive an expectation conditional maximization either (ECME) algorithm for estimating jointly the parameters of a linear regression model, of a time-variable autoregressive (AR) model with respect to the random deviations, and of a scaled t-distribution with respect to the white noise components. This algorithm is shown to take the form of iteratively reweighted least squares in the estimation of the parameters both of the regression and time-variability model. The fact that the degree of freedom of that distribution is also estimated turns the algorithm into a partially adaptive estimator. As low degrees of freedom correspond to heavy-tailed distributions, the estimator can be expected to be robust against outliers. It is shown that the initial stabilization phase of an accelerometer on a shaker table can be modeled parsimoniously and robustly by a Fourier series with AR errors for which the time-variability model is defined by cubic polynomials.

AB - We derive an expectation conditional maximization either (ECME) algorithm for estimating jointly the parameters of a linear regression model, of a time-variable autoregressive (AR) model with respect to the random deviations, and of a scaled t-distribution with respect to the white noise components. This algorithm is shown to take the form of iteratively reweighted least squares in the estimation of the parameters both of the regression and time-variability model. The fact that the degree of freedom of that distribution is also estimated turns the algorithm into a partially adaptive estimator. As low degrees of freedom correspond to heavy-tailed distributions, the estimator can be expected to be robust against outliers. It is shown that the initial stabilization phase of an accelerometer on a shaker table can be modeled parsimoniously and robustly by a Fourier series with AR errors for which the time-variability model is defined by cubic polynomials.

KW - Linear regression model, time-dependent AR process, partially adaptive estimation, robust parameter estimation, EM algorithm, iteratively reweighted least squares, scaled t-distribution

M3 - Conference contribution

SP - 1132

EP - 1145

BT - ITISE 2017

ER -