NDLI: Application of least squares variance component estimation to errors-in-variables models

Content Provider	Springer Nature Link
Author	Amiri Simkooei, A. R.
Copyright Year	2013
Abstract	In an earlier work, a simple and flexible formulation for the weighted total least squares (WTLS) problem was presented. The formulation allows one to directly apply the existing body of knowledge of the least squares theory to the errors-in-variables (EIV) models of which the complete description of the covariance matrices of the observation vector and of the design matrix can be employed. This contribution presents one of the well-known theories—least squares variance component estimation (LS-VCE)—to the total least squares problem. LS-VCE is adopted to cope with the estimation of different variance components in an EIV model having a general covariance matrix obtained from the (fully populated) covariance matrices of the functionally independent variables and a proper application of the error propagation law. Two empirical examples using real and simulated data are presented to illustrate the theory. The first example is a linear regression model and the second example is a 2-D affine transformation. For each application, two variance components—one for the observation vector and one for the coefficient matrix—are simultaneously estimated. Because the formulation is based on the standard least squares theory, the covariance matrix of the estimates in general and the precision of the estimates in particular can also be presented.
Starting Page	935
Ending Page	944
Page Count	10
File Format	PDF
ISSN	09497714
Journal	Journal of Geodesy
Volume Number	87
Issue Number	10-12
e-ISSN	14321394
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-10-08
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Weighted total least squares Errors-in-variables model Least squares variance component estimation 2-D affine transformation Geophysics/Geodesy Earth Sciences
Content Type	Text
Resource Type	Article
Subject	Geophysics Geochemistry and Petrology Computers in Earth Sciences

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