Total Least-Squares Collocation: An Optimal Estimation Technique for the EIV-Model with Prior Information

Burkhard Schaffrin
Additional contact information
Burkhard Schaffrin: Geodetic Science Program, School of Earth Sciences, The Ohio State University, Columbus, OH 43210, USA

Mathematics, 2020, vol. 8, issue 6, 1-9

Abstract: In regression analysis, oftentimes a linear (or linearized) Gauss-Markov Model (GMM) is used to describe the relationship between certain unknown parameters and measurements taken to learn about them. As soon as there are more than enough data collected to determine a unique solution for the parameters, an estimation technique needs to be applied such as ‘Least-Squares adjustment’, for instance, which turns out to be optimal under a wide range of criteria. In this context, the matrix connecting the parameters with the observations is considered fully known, and the parameter vector is considered fully unknown. This, however, is not always the reality. Therefore, two modifications of the GMM have been considered, in particular. First, ‘stochastic prior information’ (p. i.) was added on the parameters, thereby creating the – still linear – Random Effects Model (REM) where the optimal determination of the parameters (random effects) is based on ‘Least Squares collocation’, showing higher precision as long as the p. i. was adequate (Wallace test). Secondly, the coefficient matrix was allowed to contain observed elements, thus leading to the – now nonlinear – Errors-In-Variables (EIV) Model. If not using iterative linearization, the optimal estimates for the parameters would be obtained by ‘Total Least Squares adjustment’ and with generally lower, but perhaps more realistic precision. Here the two concepts are combined, thus leading to the (nonlinear) ’EIV-Model with p. i.’, where an optimal estimation (resp. prediction) technique is developed under the name of ‘Total Least-Squares collocation’. At this stage, however, the covariance matrix of the data matrix – in vector form – is still being assumed to show a Kronecker product structure.

Keywords: Errors-In-Variables Model; Total Least-Squares; prior information; collocation vs. adjustment (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/6/971/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/6/971/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:6:p:971-:d:370984

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().