On weighted total least-squares adjustment for linear regression |
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| Authors: | Burkhard Schaffrin Andreas Wieser |
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| Institution: | (1) Geodetic Science Program, The Ohio State University, Columbus, OH, USA;(2) Engineering Geodesy and Measurement Systems, Graz University of Technology, Graz, Austria |
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| Abstract: | The weighted total least-squares solution (WTLSS) is presented for an errors-in-variables model with fairly general variance–covariance
matrices. In particular, the observations can be heteroscedastic and correlated, but the variance–covariance matrix of the
dependent variables needs to have a certain block structure. An algorithm for the computation of the WTLSS is presented and
applied to a straight-line fit problem where the data have been observed with different precision, and to a multiple regression
problem from recently published climate change research. |
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| Keywords: | Total least-squares solution (TLSS) Errors-in-variables model Weight matrix Heteroscedastic observations Straight-line fit Multiple linear regression |
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