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Asymptotics for weakly dependent errors-in-variables. (English) Zbl 1278.15036
Summary: Linear relations, containing measurement errors in input and output data, are taken into account in this paper. Parameters of these so-called errors-in-variables (EIV) models can be estimated by minimizing the total least squares (TLS) of the input-output disturbances. Such an estimate is highly non-linear. Moreover in some realistic situations, the errors cannot be considered as independent by nature. Weakly dependent ($$\alpha$$- and $$\varphi$$-mixing) disturbances, which are not necessarily stationary nor identically distributed, are considered in the EIV model. Asymptotic normality of the TLS estimate is proved under some reasonable stochastic assumptions on the errors. Derived asymptotic properties provide necessary basis for the validity of block-bootstrap procedures.

##### MSC:
 15B51 Stochastic matrices 15B52 Random matrices (algebraic aspects) 62E20 Asymptotic distribution theory in statistics 62J99 Linear inference, regression 65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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