On weighted total least-squares adjustment for linear regression
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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.
KeywordsTotal least-squares solution (TLSS) Errors-in-variables model Weight matrix Heteroscedastic observations Straight-line fit Multiple linear regression
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- 2.Golub GH, van Loan Ch (1996) Matrix computations, 3rd edn. Johns Hopkins University Press, BaltimoreGoogle Scholar
- 3.Grafarend E, Schaffrin B (1993) Adjustment computations in linear models (in German). Bibliographical Institute, Mannheim, GermanyGoogle Scholar
- 4.Magnus JR, Neudecker H (1988) Matrix differential calculus with applications in statistics and econometrics. Wiley, New YorkGoogle Scholar
- 5.Mann ME, Emanuel KA (2006) Atlantic hurricane trends linked to climate change. EOS 87–24: 233–241Google Scholar
- 8.Pope AJ (1972) Some pitfalls to be avoided in the iterative adjustment of nonlinear problems. In: Proc 38th Ann Meet Am Soc Phot, Washington, DC, pp 449–473Google Scholar
- 9.Schaffrin B, Wang Z (1995) Multiplicative outlier search using homBLUP and an equivalence theorem. Manus Geodaet 20: 21–26Google Scholar
- 10.Schaffrin B, Lee IP, Felus Y, Choi YS (2006) Total least-squares for geodetic straight-line and plane adjustment. Boll Geod Sci Aff 65: 141–168Google Scholar
- 11.Schaffrin B, Felus Y (2007) Multivariate total-least squares adjustment for empirical affine transformations. In: Proc 6th Hotine-Marussi Symp, Wuhan, People’s Republic of China, May, forthcomingGoogle Scholar
- 13.van Huffel S, Vandewalle J (1991) The total least-squares problem. Computational aspects and analysis. SIAM, PhiladelphiaGoogle Scholar