Consistency of the total least squares estimator in the linear errors-in-variables regression

被引：2

作者：

Shklyar, Sergiy ^{[1
]}

机构：

[1] Taras Shevchenko Natl Univ Kyiv, Kiev, Ukraine

来源：

MODERN STOCHASTICS-THEORY AND APPLICATIONS | 2018年 / 5卷 / 03期

关键词：

Errors in variables; functional model; linear regression; measurement error model; multivariate regression; total least squares; strong consistency;

D O I：

10.15559/18-VMSTA104

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper deals with a homoskedastic errors-in-variables linear regression model and properties of the total least squares (TLS) estimator. We partly revise the consistency results for the TLS estimator previously obtained by the author [18]. We present complete and comprehensive proofs of consistency theorems. A theoretical foundation for construction of the TLS estimator and its relation to the generalized eigenvalue problem is explained. Particularly, the uniqueness of the estimate is proved. The Frobenius norm in the definition of the estimator can be substituted by the spectral norm, or by any other unitarily invariant norm; then the consistency results are still valid.

引用

页码：247 / 295

页数：49

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