Geodetic Institute
Logo Geodetic Institute

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

authored by
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.

Organisation(s)
Geodetic Institute
Type
Article
Journal
Journal of geodesy
Volume
92
Pages
271-297
No. of pages
27
ISSN
0949-7714
Publication date
09.09.2017
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Geophysics, Geochemistry and Petrology, Computers in Earth Sciences
Electronic version(s)
https://doi.org/10.1007/s00190-017-1062-6 (Access: Closed)
 

Details in the research portal "Research@Leibniz University"