SIAM Journal on Matrix Analysis and Applications
Overview of total least-squares methods
Signal Processing
Editorial: Total Least Squares and Errors-in-variables Modeling
Computational Statistics & Data Analysis
Local influence assessment in heteroscedastic measurement error models
Computational Statistics & Data Analysis
Editorial: 2nd Special issue on matrix computations and statistics
Computational Statistics & Data Analysis
Approximate low-rank factorization with structured factors
Computational Statistics & Data Analysis
On weighted structured total least squares
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
| Hi-index | 0.03 |
A new technique is considered for parameter estimation in a linear measurement error model AX~B, A=A"0+A@?, B=B"0+B@?, A"0X"0=B"0 with row-wise independent and non-identically distributed measurement errors A@?, B@?. Here, A"0 and B"0 are the true values of the measurements A and B, and X"0 is the true value of the parameter X. The total least-squares method yields an inconsistent estimate of the parameter in this case. Modified total least-squares problem, called element-wise weighted total least-squares, is formulated so that it provides a consistent estimator, i.e., the estimate X@^ converges to the true value X"0 as the number of measurements increases. The new estimator is a solution of an optimization problem with the parameter estimate X@^ and the correction @DD=[@DA@DB], applied to the measured data D=[AB], as decision variables. An equivalent unconstrained problem is derived by minimizing analytically over the correction @DD, and an iterative algorithm for its solution, based on the first order optimality condition, is proposed. The algorithm is locally convergent with linear convergence rate. For large sample size the convergence rate tends to quadratic.