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Consistency of elementwise-weighted total least squares estimator in a multivariate errors-in-variables model AX=B

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  • Alexander Kukush
  • Sabine Van Huffel

Abstract

A multivariate measurement error model AX≈B is considered. The errors in [A,B] are rowwise independent, but within each row the errors may be correlated. Some of the columns are observed without errors, and in addition the error covariance matrices may differ from row to row. The total covariance structure of the errors is supposed to be known up to a scalar factor. The fully weighted total least squares estimator of X is studied, which in the case of normal errors coincides with the maximum likelihood estimator. We give mild conditions for weak and strong consistency of the estimator, when the number of rows in A increases. The results generalize the conditions of Gallo given for a univariate homoscedastic model (where B is a vector), and extend the conditions of Gleser given for the multivariate homoscedastic model. We derive the objective function for the estimator and propose an iteratively reweighted numerical procedure. Copyright Springer-Verlag 2004

Suggested Citation

  • Alexander Kukush & Sabine Van Huffel, 2004. "Consistency of elementwise-weighted total least squares estimator in a multivariate errors-in-variables model AX=B," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(1), pages 75-97, February.
    • Handle: RePEc:spr:metrik:v:59:y:2004:i:1:p:75-97
    DOI: 10.1007/s001840300272
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    Citations

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    Cited by:

    1. Milan Hladík & Michal Černý & Jaromír Antoch, 2020. "EIV regression with bounded errors in data: total ‘least squares’ with Chebyshev norm," Statistical Papers, Springer, vol. 61(1), pages 279-301, February.
    2. de Castro, Mario & Galea-Rojas, Manuel & Bolfarine, Heleno, 2007. "Local influence assessment in heteroscedastic measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1132-1142, October.
    3. Kukush, A. & Markovsky, I. & Van Huffel, S., 2007. "Estimation in a linear multivariate measurement error model with a change point in the data," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1167-1182, October.
    4. Michal Pešta, 2016. "Unitarily invariant errors-in-variables estimation," Statistical Papers, Springer, vol. 57(4), pages 1041-1057, December.
    5. Markovsky, Ivan & Luisa Rastello, Maria & Premoli, Amedeo & Kukush, Alexander & Van Huffel, Sabine, 2006. "The element-wise weighted total least-squares problem," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 181-209, January.

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