【摘 要】
：
For a straight line in 2D, it is well known that the Total Least-Squares (TLS) estimator within an Errors-In-Variables (EIV) model generates the same soluti
【机 构】
：
GeodeticScienceProgram,SchoolofEarthSciences,TheOhioStateUniversity,Columbus,Ohio,USAGeodeticScience
【出 处】
：
The 24th International Workshop on Matrices and Statistics(第
论文部分内容阅读
For a straight line in 2D, it is well known that the Total Least-Squares (TLS) estimator within an Errors-In-Variables (EIV) model generates the same solution as orthogonal regression, which turns out to be (locally) unbiased; see, e.g., Schaffrin and Wieser (2008) who treated the 2D line there. Unfortunately, however, the adjustment of a conic section (such as a parabola in 2D) will, if based on orthogonal regression, be biased within the standard EIV model. Here, an approach will be investigated where TLS estimation is applied to a modified EIV model in order to account for the bias that must otherwise be expected. The effect of such "bias reduction" will be illuminated in a realistic example from geodesy, taken out of a textbook by Mikhail and Gracie (1981).
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