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An iteratively reweighted least-squares approach to adaptive robust adjustment of parameters in linear regression models with autoregressive and t-distributed deviations

verfasst von
Boris Kargoll, Mohammad Omidalizarandi, Ina Loth, Jens-André Paffenholz, Hamza Alkhatib
Abstract

In this paper, we investigate a linear regression time series model of possibly outlier-afflicted observations and autocorrelated random deviations. This colored noise is represented by a covariance-stationary autoregressive (AR) process, in which the independent error components follow a scaled (Student’s) t-distribution. This error model allows for the stochastic modeling of multiple outliers and for an adaptive robust maximum likelihood (ML) estimation of the unknown regression and AR coefficients, the scale parameter, and the degree of freedom of the t-distribution. This approach is meant to be an extension of known estimators, which tend to focus only on the regression model, or on the AR error model, or on normally distributed errors. For the purpose of ML estimation, we derive an expectation conditional maximization either algorithm, which leads to an easy-to-implement version of iteratively reweighted least squares. The estimation performance of the algorithm is evaluated via Monte Carlo simulations for a Fourier as well as a spline model in connection with AR colored noise models of different orders and with three different sampling distributions generating the white noise components. We apply the algorithm to a vibration dataset recorded by a high-accuracy, single-axis accelerometer, focusing on the evaluation of the estimated AR colored noise model.

Organisationseinheit(en)
Geodätisches Institut
Typ
Artikel
Journal
Journal of geodesy
Band
92
Seiten
271-297
Anzahl der Seiten
27
ISSN
0949-7714
Publikationsdatum
09.09.2017
Publikationsstatus
Veröffentlicht
Peer-reviewed
Ja
ASJC Scopus Sachgebiete
Geophysik, Geochemie und Petrologie, Computer in den Geowissenschaften
Elektronische Version(en)
https://doi.org/10.1007/s00190-017-1062-6 (Zugang: Geschlossen)
 

Details im Forschungsportal „Research@Leibniz University“