Univariate regression models with errors in both axes

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Abstract
Calibration is a fundamental step in the calculation of the unknown concentration of analyte in most analytical methods. It is known that for certain methodologies, if only the errors in the independent variable are taken into account, there may be considerable errors in the estimation of the value of the regression coefficients, the derived statistical parameters and in some cases the sought for response and concentration values. This paper reviews the calibration methods including some references to procedures for the detection of outliers and robust regression when there are errors in both axes. The advantages and limitations of the different approaches are discussed and a comparative study is made of the approaches of several techniques for which computer programmes have been developed based on the algorithms put forward by the different authors. Finally, some trends of future development in this field are envisaged.

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