Geodesic
Asymptotic normality of element-wise weighted total least squares estimator in a multivariate errors-in-variables model
Teoriâ slučajnyh processov, Tome 21 (2016) no. 2, pp. 96-105.

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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.
Keywords: Asymptotic normality, element-wise weighted total least squares estimator, heteroscedastic errors, multivariate errors-in-variables model. 
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Ya. V. Tsaregorodtsev. Asymptotic normality of element-wise weighted total least squares estimator in a multivariate errors-in-variables model. Teoriâ slučajnyh processov, Tome 21 (2016) no. 2, pp. 96-105. http://geodesic.mathdoc.fr/item/THSP_2016_21_2_a8/

[1] R. J. Carroll, D. Ruppert, L. A. Stefanski, C. M. Crainiceanu, Measurement Error in Nonlinear Models: A Modern Perspective, 2nd ed., Chapman and Hall/CRC, Boca Raton, 2006

[2]

[3] L. J. Gleser, “Estimation in a multivariate “errors in variables” regression model: large sample results”, Ann. Stat., 9:1 (1981), 24–44

[4] G. H. Golub, C. F. Van Loan, “An analysis of the total least squares problem”, SIAM J. Numer. Anal., 17:6 (1980), 883–893

[5] S. Jazaerti, A. R. Amiri-Simkooei, M. A. Sharifi, “Iterative algorithm for weighted total least squares adjustment”, Survey Review, 46:334 (2014), 19–27

[6] A. Kukush, S. Van Huffel, “Consistency of elementwise-weighted total least squares estimator in a multivariate errors-in-variables model $AX = B$”, Metrika, 59:1 (2004), 75–97

[7] A. Kukush, Ya. Tsaregorodtsev, “Asymptotic normality of total least squares estimator in a multivariable errors-in-variables model $AX=B$”, Modern Stochastics: Theory and Applications, 3:1 (2016), 47–57

[8] A. Kukush, Ya. Tsaregorodtsev, “Goodness-of-fit test in a multivariate errors-in-variables model $AX = B$”, Modern Stochastics: Theory and Applications, 3:4 (2016), 287–302

[9] V. Mahboud, “On weighted total least squares for geodetic transformation”, J. of Geodesy, 86:5 (2012), 359–367

[10] I. Markovsky, M. L. Rastello, A. Premoli, A. Kukush, S. Van Huffel, “The element-wise weighted total least-squares problem”, Comput. Statist. Data Anal., 50:1 (2006), 181–209

[11] G. Pfanzagl, “On the measurability and consistency of minimum contrast estimates”, Metrika, 14:1 (1969), 249–273

[12] S. Van Huffel, J. Vandewalle, The Total Least Squares Problem: Computational Aspects and Analysis, Frontiers in Applied Mathematics, 9, SIAM, Philadelphia, PA, 1991