Tsaregorodtsev, Ya. V. Asymptotic normality of element-wise weighted total least squares estimator in a multivariate errors-in-variables model. (English) Zbl 1374.62014 Theory Stoch. Process. 21, No. 2, 96-105 (2016). Summary: A multivariable measurement error model \(AX \approx B\) is considered. Here \(A\) and \(B\) are input and output matrices of measurements and \(X\) is a rectangular matrix of fixed size to be estimated. The errors in \([A,B]\) are row-wise independent, but within each row the errors may be correlated. Some of the columns are observed without errors and the error covariance matrices may differ from row to row. The total covariance structure of the errors is known up to a scalar factor. The fully weighted total least squares estimator of \(X\) is studied. We give conditions for asymptotic normality of the estimator, as the number of rows in \(A\) is increasing. We provide that the covariance structure of the limiting Gaussian random matrix is nonsingular. MSC: 62E20 Asymptotic distribution theory in statistics 62F12 Asymptotic properties of parametric estimators 62J05 Linear regression; mixed models 62H12 Estimation in multivariate analysis 65F20 Numerical solutions to overdetermined systems, pseudoinverses Keywords:asymptotic normality; element-wise weighted total least squares estimator; heteroscedastic errors; multivariate errors-in-variables model PDFBibTeX XMLCite \textit{Ya. V. Tsaregorodtsev}, Theory Stoch. Process. 21, No. 2, 96--105 (2016; Zbl 1374.62014) Full Text: arXiv Link