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Variance components in errors-in-variables models: estimability, stability and bias analysis
Abstract Although total least squares has been substantially investigated theoretically and widely applied in practical applications, almost nothing has been done to simultaneously address the estimation of parameters and the errors-in-variables (EIV) stochastic model. We prove that the variance components of the EIV stochastic model are not estimable, if the elements of the random coefficient matrix can be classified into two or more groups of data of the same accuracy. This result of inestimability is surprising as it indicates that we have no way of gaining any knowledge on such an EIV stochastic model. We demonstrate that the linear equations for the estimation of variance components could be ill-conditioned, if the variance components are theoretically estimable. Finally, if the variance components are estimable, we derive the biases of their estimates, which could be significantly amplified due to a large condition number.
Variance components in errors-in-variables models: estimability, stability and bias analysis
Abstract Although total least squares has been substantially investigated theoretically and widely applied in practical applications, almost nothing has been done to simultaneously address the estimation of parameters and the errors-in-variables (EIV) stochastic model. We prove that the variance components of the EIV stochastic model are not estimable, if the elements of the random coefficient matrix can be classified into two or more groups of data of the same accuracy. This result of inestimability is surprising as it indicates that we have no way of gaining any knowledge on such an EIV stochastic model. We demonstrate that the linear equations for the estimation of variance components could be ill-conditioned, if the variance components are theoretically estimable. Finally, if the variance components are estimable, we derive the biases of their estimates, which could be significantly amplified due to a large condition number.
Variance components in errors-in-variables models: estimability, stability and bias analysis
Xu, Peiliang (author) / Liu, Jingnan (author)
Journal of Geodesy ; 88
2014
Article (Journal)
English
BKL:
38.73
Geodäsie
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