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.

翻译：本文构建了变量含误差线性回归模型的估计量。该回归模型导致一类具有行约束与列约束的总体最小二乘问题。尽管该问题可通过数值方法求解，但尚不清楚其解是否具有统计意义上的相合性。通过利用正交投影及其性质，本文所提出的估计量可自然构造，其强相合性得以严格证明。此外，我们的渐近分析还证明了该类带行、列约束的总体最小二乘问题解的强相合性。