CONSISTENCY OF THE ORTHOGONAL REGRESSION ESTIMATOR IN AN IMPLICIT LINEAR MODEL WITH ERRORS IN VARIABLES

摘要

An implicit linear regression model with errors in variables is studied for which the true points belong to a certain hyperplane in Euclidean space and the joint covariance matrix of errors is proportional to the unit matrix. The orthogonal regression estimator for this hyperplane is considered. Some sufficient conditions for the consistency as well as for the strong consistency are given. Some applications to the explicit multiple regression model with a free term and errors in variables are shown.