Total Msplit estimation

M-split estimation is a method that enables the estimation of mutually competing versions of parameters in functional observation models. In the presented study, the classical functional models found in it are replaced by errors-in-variables (EIV) models. Similar to the weighted total least-squares (WTLS) method, the random components of these models were assigned covariance matrix models. Thus, the proposed method, named Total M-split (TMsplit) estimation, corresponds to the basic rules of WTLS. TMsplit estimation objective function is constructed using the components of squared M-split and WTLS estimation objective functions. The TMsplit estimation algorithm is based on the Gauss-Newton method that is applied using a linear approximation of EIV models. The basic properties of the method are presented using examples of the estimation of regression line parameters and the estimation of parameters in a two-dimensional affine transformation.

Automated summary

M-split estimation is a method that allows the estimation of mutually competing versions of parameters in functional observation models by replacing classical functional models with errors-in-variables (EIV) models. The proposed Total M-split (TMsplit) estimation method follows the basic principles of weighted total least-squares (WTLS) and constructs an objective function using squared M-split and WTLS estimation objective functions. The TMsplit estimation algorithm is based on the Gauss-Newton method with a linear approximation of EIV models. The method's basic properties are demonstrated through examples of regression line parameter estimation and two-dimensional affine transformation parameter estimation.