A bound for the Euclidean norm of the difference between the best linear unbiased estimator and a linear unbiased estimator |
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| Authors: | J Mäkinen |
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| Institution: | (1) Finnish Geodetic Institute, P.O. Box 15, 02431 Masala, Finland e-mail: jaakko.makinen@fgi.fi; Tel.:+358-9-295550; Fax:+358-9-29555200, FI |
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| Abstract: | A bound is established for the Euclidean norm of the difference between the best linear unbiased estimator and any linear
unbiased estimator in the general linear model. The bound involves the spectral norm of the difference between the dispersion
matrices of the two estimators, and the residual sum of squares, all evaluated at the assumed model, but is independent of
the provenance of the observation vector at hand. The bound, a straightforward consequence of first principles in Gauss–Markov
theory, generalizes previous results on the difference between the best linear unbiased estimator and the ordinary least-squares
estimator. In a numerical example from repeated precise levelling, the bound is used to analyse the sensitivity of estimates
of vertical motion to the choice of estimator.
Received: 9 September 1999 / Accepted: 15 March 2002 |
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| Keywords: | : Linear model – Least-squares estimate – Best linear unbiased estimate – Gauss– Markov estimate – Spectral norm – Precise levelling – Vertical motion |
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