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：在本文中, 我们构建了一个可变误线性回归模型的估测符。 回归模型在行和列的限制下导致一个受限制的最小方块的问题。 虽然这个问题可以用数字方式解决, 但它在统计意义上是否一致尚不得而知。 提议的估算符可以通过使用正方形预测及其属性来构建, 它的强烈一致性是自然得到证明的。 此外, 我们的无症状分析证明, 问题的全部最小方块解决方案与行和列的限制非常一致。