Consistent estimation with the use of orthogonal projections for a linear regression model with errors in the variables

TL;DR

This paper introduces a new estimator for errors-in-variables linear regression models using orthogonal projections, demonstrating its strong consistency and providing asymptotic analysis for constrained total least squares solutions.

Contribution

It presents a novel estimator based on orthogonal projections for errors-in-variables models and proves its strong consistency and asymptotic properties.

Findings

Estimator is strongly consistent.

Asymptotic analysis confirms consistency of constrained total least squares.

Provides theoretical foundation for numerical solutions.

Abstract

In this paper, we construct an estimator of an errors-in-variables linear regression model. The regression model leads to a constrained total least squares problems with row and column constraints. Although this problem can be numerically solved, it is unknown whether the solution has consistency in the statistical sense. The proposed estimator can be constructed by the use of orthogonal projections and their properties, its strong consistency is naturally proved. Moreover, our asymptotic analysis proves the strong consistency of the total least squares solution of the problem with row and column constraints.