Abstract
In this contribution, we consider an expectation conditional maximization either (ECME) algorithm for the purpose of estimating the parameters of a linear observation model with time-dependent autoregressive (AR) errors. The degree of freedom (d.o.f.) of the underlying family of scaled t-distributions, which is used to account for outliers and heavy-tailedness of the white noise components, is adapted to the data, resulting in a self-tuning robust estimator. The time variability of the AR coefficients is described by a second linear model. We improve the estimation of the d.o.f. in a previous version of the ECME algorithm, which involves a zero search, by using an interval Newton method. We model the transient oscillations of a shaker table measured by a high-accuracy accelerometer, and we analyze various criteria for selecting a simultaneously parsimonious and realistic time-variability model.
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Acknowledgements
The presented application of the PCB Piezotronics accelerometer within the vibration analysis experiment was performed as a part of the collaborative project “Spatio-temporal monitoring of bridge structures using low cost sensors” with ALLSAT GmbH, which is funded by the German Federal Ministry for Economic Affairs and Energy (BMWi) and the Central Innovation Programme for SMEs (ZIM Kooperationsprojekt, ZF4081803DB6). In addition, the authors acknowledge the Institute of Concrete Construction (Leibniz Universität Hannover) for providing the shaker table and the reference accelerometer.
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Kargoll, B., Omidalizarandi, M., Alkhatib, H., Schuh, WD. (2018). Further Results on a Modified EM Algorithm for Parameter Estimation in Linear Models with Time-Dependent Autoregressive and t-Distributed Errors. In: Rojas, I., Pomares, H., Valenzuela, O. (eds) Time Series Analysis and Forecasting. ITISE 2017. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-96944-2_22
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