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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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VTeX
2016-03-01
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| Series: | Modern Stochastics: Theory and Applications |
| Subjects: | |
| Online Access: | https://vmsta.vtex.vmt/doi/10.15559/16-VMSTA50 |
| Summary: | 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. |
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| ISSN: | 2351-6046 2351-6054 |