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Asymptotic normality of element-wise weighted total least squares estimator in a multivariate errors-in-variables model. (English) Zbl 1374.62014

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
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