Geodesic
On the Equivalence between Orthogonal Regression and Linear Model with Type-II Constraints
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 2, pp. 19-27.

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Orthogonal regression, also known as the total least squares method, regression with errors-in variables or as a calibration problem, analyzes linear relationship between variables. Comparing to the standard regression, both dependent and explanatory variables account for measurement errors. Through this paper we shortly discuss the orthogonal least squares, the least squares and the maximum likelihood methods for estimation of the orthogonal regression line. We also show that all mentioned approaches lead to the same estimates in a special case.
Classification : 62F10, 62J05
Keywords: linear regression model with type-II constraints; orthogonal regression; estimation 
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Donevska, Sandra; Fišerová, Eva; Hron, Karel. On the Equivalence between Orthogonal Regression and Linear Model with Type-II Constraints. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 2, pp. 19-27. http://geodesic.mathdoc.fr/item/AUPO_2011__50_2_a2/