Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">A</mi><mi mathvariant="italic">X</mi><mo>=</mo><mi mathvariant="italic">B</mi></math>
We consider a multivariate functional measurement error model $AX\approx B$. The errors in $[A,B]$ are uncorrelated, row-wise independent, and have equal (unknown) variances. We study the total least squares estimator of X, which, in the case of normal errors, coincides with the maximum likelihood o...
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| Language: | English |
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2016-03-01
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| Series: | Modern Stochastics: Theory and Applications |
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| Online Access: | https://vmsta.vtex.vmt/doi/10.15559/16-VMSTA50 |
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doaj-bf6bf9fab08a44f199923656fb74a8962020-11-25T01:18:13ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542016-03-0131475710.15559/16-VMSTA50Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">A</mi><mi mathvariant="italic">X</mi><mo>=</mo><mi mathvariant="italic">B</mi></math>Alexander Kukush0Yaroslav Tsaregorodtsev1Taras Shevchenko National University of Kyiv, Kyiv, UkraineTaras Shevchenko National University of Kyiv, Kyiv, UkraineWe consider a multivariate functional measurement error model $AX\approx B$. The errors in $[A,B]$ are uncorrelated, row-wise independent, and have equal (unknown) variances. We study the total least squares estimator of X, which, in the case of normal errors, coincides with the maximum likelihood one. We give conditions for asymptotic normality of the estimator when the number of rows in A is increasing. Under mild assumptions, the covariance structure of the limit Gaussian random matrix is nonsingular. For normal errors, the results can be used to construct an asymptotic confidence interval for a linear functional of X.https://vmsta.vtex.vmt/doi/10.15559/16-VMSTA50Asymptotic normalitymultivariate errors-in-variables modeltotal least squares |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Alexander Kukush Yaroslav Tsaregorodtsev |
| spellingShingle |
Alexander Kukush Yaroslav Tsaregorodtsev Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">A</mi><mi mathvariant="italic">X</mi><mo>=</mo><mi mathvariant="italic">B</mi></math> Modern Stochastics: Theory and Applications Asymptotic normality multivariate errors-in-variables model total least squares |
| author_facet |
Alexander Kukush Yaroslav Tsaregorodtsev |
| author_sort |
Alexander Kukush |
| title |
Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">A</mi><mi mathvariant="italic">X</mi><mo>=</mo><mi mathvariant="italic">B</mi></math> |
| title_short |
Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">A</mi><mi mathvariant="italic">X</mi><mo>=</mo><mi mathvariant="italic">B</mi></math> |
| title_full |
Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">A</mi><mi mathvariant="italic">X</mi><mo>=</mo><mi mathvariant="italic">B</mi></math> |
| title_fullStr |
Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">A</mi><mi mathvariant="italic">X</mi><mo>=</mo><mi mathvariant="italic">B</mi></math> |
| title_full_unstemmed |
Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="italic">A</mi><mi mathvariant="italic">X</mi><mo>=</mo><mi mathvariant="italic">B</mi></math> |
| title_sort |
asymptotic normality of total least squares estimator in a multivariate errors-in-variables model <math xmlns="http://www.w3.org/1998/math/mathml"><mi mathvariant="italic">a</mi><mi mathvariant="italic">x</mi><mo>=</mo><mi mathvariant="italic">b</mi></math> |
| publisher |
VTeX |
| series |
Modern Stochastics: Theory and Applications |
| issn |
2351-6046 2351-6054 |
| publishDate |
2016-03-01 |
| description |
We consider a multivariate functional measurement error model $AX\approx B$. The errors in $[A,B]$ are uncorrelated, row-wise independent, and have equal (unknown) variances. We study the total least squares estimator of X, which, in the case of normal errors, coincides with the maximum likelihood one. We give conditions for asymptotic normality of the estimator when the number of rows in A is increasing. Under mild assumptions, the covariance structure of the limit Gaussian random matrix is nonsingular. For normal errors, the results can be used to construct an asymptotic confidence interval for a linear functional of X. |
| topic |
Asymptotic normality multivariate errors-in-variables model total least squares |
| url |
https://vmsta.vtex.vmt/doi/10.15559/16-VMSTA50 |
| work_keys_str_mv |
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