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

Metrika ◽  
2004 ◽  
Vol 59 (1) ◽  
pp. 75-97 ◽  
Author(s):  
Alexander Kukush ◽  
Sabine Van Huffel
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Least Squares Estimator ◽  
Errors In Variables ◽  
Weighted Total Least Squares

scholarly journals Scaled weighted total least-squares adjustment for partial errors-in-variables model

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
J. Zhao
Keyword(s):  
Least Squares ◽  
Variance Component ◽  
Maximum Likelihood Method ◽  
Coefficient Matrix ◽  
Total Least Squares ◽  
Likelihood Method ◽  
Errors In Variables ◽  
Weighted Total Least Squares ◽  
Least Squares Adjustment ◽  
Observation Vector

AbstractScaled total least-squares (STLS) unify LS, Data LS, and TLS with a different choice of scaled parameter. The function of the scaled parameter is to balance the effect of random error of coefficient matrix and observation vector for the estimate of unknown parameter. Unfortunately, there are no discussions about how to determine the scaled parameter. Consequently, the STLS solution cannot be obtained because the scaled parameter is unknown. In addition, the STLS method cannot be applied to the structured EIV casewhere the coefficient matrix contains the fixed element and the repeated random elements in different locations or both. To circumvent the shortcomings above, the study generalize it to a scaledweighted TLS (SWTLS) problem based on partial errors-in-variable (EIV) model. And the maximum likelihood method is employed to derive the variance component of observations and coefficient matrix. Then the ratio of variance component is proposed to get the scaled parameter. The existing STLS method and WTLS method is just a special example of the SWTLS method. The numerical results show that the proposed method proves to bemore effective in some aspects.

Bootstrapped Total Least Squares estimator using (circular) overlap for Errors-In-Variables identification

2009 ◽  
Vol 42 (10) ◽  
pp. 1568-1573
Author(s):  
Gerd Vandersteen ◽  
Kurt Barbé ◽  
Rik Pintelon ◽  
Johan Schoukens
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Least Squares Estimator ◽  
Errors In Variables
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