On the trade-off between model expansion, model shrinking, and parameter estimation accuracy in least-squares data analysis

• Published in: Journal of geodesy 2005-11, Vol.79 (8), p.460-466
• Main Author: KOTSAKIS, C
• Format: Article
• Language: English
• Subjects: Earth sciences; Earth, ocean, space; Exact sciences and technology; Geodetics; Internal geophysics; Mathematical models; Solid-earth geophysics, tectonophysics, gravimetry; Studies
• ISSN: 0949-7714; 1432-1394
• DOI: 10.1007/s00190-005-0479-5

A systematic investigation of over-parameterized and under-parameterized formulations in the least-squares adjustment of linear models is performed in this paper. Over-parameterization and under-parameterization are modeling effects that can often occur in the adjustment of geodetic data. The former refers to situations where new unknown parameters are added to an existing model in order to provide a more precise deterministic description for a given data set. Such an expansion may either correspond to a physically meaningful and necessary model improvement (e.g. due to the presence of unknown systematic errors in the input data) or to a fabricated data over-fitting through the inclusion of fictitious parametric terms in the mathematical model for the data adjustment. On the other hand, under-parameterization schemes emerge when the effects of existing systematic disturbances are omitted from the mathematical model that is employed for the data adjustment, thus causing a bias in the estimates for the remaining model parameters. The main focus of this study is the statistical accuracy of the estimated model parameters and the conditions under which it can be improved, either through an over-parameterized model formulation or through an under-parameterized model formulation.[PUBLICATION ABSTRACT]