V. G. Zaycev, Lead Engineer, e-mail: zaycev@looch.ru, Scientific Production Enterprise of Geophysical Equipment "Looch" Novosibirsk, 630051, Russian Federation

To Evaluation of Parameters of Models at Presence of Errors in Entrance and Output Variables. Linear Case

This paper presents the ways to identify systems described by models with errors in recording of input and output variables. It is considered that in the absence of information on the error parameters in the case of their large values, it is impossible to obtain acceptable estimates of all the required parameters of the model without additional, in comparison with the regression analysis, assumptions. The determination of the regression parameters in the presence of errors in the input and output variables is impor­tant for solving many tasks related to data processing. In all existing approaches, either the assumptions regarding the noise in the form of e.g. given relations between the noises dispersions are made, or the method of successive approximations is applied. To determine the parameters of the linear function, it is proposed to use the condition of the symmetry of the joint probability density of the observed input and output variables in the oblique coordinates. For the case of normality of the noise, the article gives a formula for determining the parameter of the relationship via the estimates of the fourth-order semi-invariants.
Keywords: structural analysis, symmetric distribution of hindrances, oblique-angled system of coordinates, solvency of estimation

P. 555–563