Total Msplit estimation
Z. Wiśniewski
Abstract
Abstract 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 (TM split ) estimation, corresponds to the basic rules of WTLS. TM split estimation objective function is constructed using the components of squared M split and WTLS estimation objective functions. The TM split 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.