Least-squares adjustment taking into account the errors in variables

Fourth Total Least Squares and Errors-in-Variables Modeling Workshop

Total least squares and errors-in-variables modeling

The main purpose of this special issue is to present an overview of the progress of a modeling technique which is known as total least squares (TLS) in computational mathematics and engineering, and as errors-in-variables (EIV) modeling or orthogonal regression in the statistical community. The TLS method is one of several linear parameter estimation techniques that has been devised to compensa...

Least-Squares Covariance Matrix Adjustment

We consider the problem of finding the smallest adjustment to a given symmetric n × n matrix, as measured by the Euclidean or Frobenius norm, so that it satisfies some given linear equalities and inequalities, and in addition is positive semidefinite. This least-squares covariance adjustment problem is a convex optimization problem, and can be efficiently solved using standard methods when the ...

Consistency of the structured total least squares estimator in a multivariate errors-in-variables model

The structured total least squares estimator, defined via a constrained optimization problem, is a generalization of the total least squares estimator when the data matrix and the applied correction satisfy given structural constraints. In the paper, an affine structure with additional assumptions is considered. In particular, Toeplitz and Hankel structured, noise free and unstructured blocks a...

Estimating Errors in Least-Squares Fitting

While least-squares fitting procedures are commonly used in data analysis and are extensively discussed in the literature devoted to this subject, the proper assessment of errors resulting from such fits has received relatively little attention. The present work considers statistical errors in the fitted parameters, as well as in the values of the fitted function itself, resulting from random e...