Introduction to Total Least Squares and Errors-In-Variables Modeling

Huffel, Sabine Van; Lemmerling, Philippe

doi:10.1007/978-94-017-3552-0_1

Cited by 32 publications

(41 citation statements)

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“…RMA is one of a class of similar models known as orthogonal regression, total least squares regression, or errors-in-variables modeling, depending on the discipline in which the specific technique was developed (Van Huffel, 1997). Orthogonal regression minimizes the sum of squared orthogonal distances from measurement points to the model function.…”

Section: Regression and Related Analysismentioning

confidence: 99%

“…The RMA version of orthogonal regression is graphically depicted in Curran and Hay (1986). Van Huffel (1997) contains examples of orthogonal regression's usage in astronomy, meteorology, 3-D motion estimation, biomedical signal processing, and multivariate calibration. RMA, specifically, is quite commonly applied in allometry (Conrad & Gutmann, 1996;Gower, Kucharik, & Norman, 1999;Nicol & Mackauer, 1999;Niklas & Buckman, 1994).…”

Section: Regression and Related Analysismentioning

confidence: 99%

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An improved strategy for regression of biophysical variables and Landsat ETM+ data

Cohen

Maiersperger

Gower

et al. 2003

Remote Sensing of Environment

378

235

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Section: Regression and Related Analysismentioning

confidence: 99%

Section: Regression and Related Analysismentioning

confidence: 99%

An improved strategy for regression of biophysical variables and Landsat ETM+ data

Cohen

Maiersperger

Gower

et al. 2003

Remote Sensing of Environment

378

235

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“…LetΘ = (â,b,R) denote the MLE of the circle parameters (center and radius). We denote byũ andṽ two vectors whose components are defined by (19)…”

Section: Validation Of Our Approximative Formulasmentioning

confidence: 99%

“…Regression models in which all variables are subject to errors are known as errors-invariables (EIV) models [8,12,19]. The EIV regression problem is quite different (and far more difficult) than the classical regression where the independent variable is assumed to be error-free.…”

Section: Introductionmentioning

confidence: 99%

Untitled

2012

Theor. Probability and Math. Statist.

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Abstract. Regression models in which all variables are subject to errors are known as errors-in-variables (EIV) models. The respective parameter estimates have many unusual properties: their exact distributions are very hard to determine, and their absolute moments are often infinite (so that their mean and variance do not exist). In our paper, Error analysis for circle fitting algorithms, Electr. J. Stat. 3 (2009), 886-911, we developed an unconventional statistical analysis that allowed us to effectively assess EIV parameter estimates and design new methods with superior characteristics. In this paper we validate our approach in a series of numerical tests. We also prove that in the case of fitting circles, the estimates of the parameters are absolutely continuous (have densities).

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“…In order to keep our analysis coherent with the concept of simultaneous dimensionality reduction, retained variance maximization and approximation error minimization, we do not invite the reader to such geometric intuitions. Note that the error minimization framework can also be viewed as a total least squares regression problem with all variables thought to be free so that the task is to fit a lower dimensional hyperplane that minimizes the perpendicular distances from the data points to the hyperplane (Van Huffel, 1997). We will also be reviewing (Bishop, 2006) who derives PCA in the same framework as that of ours.…”

Section: Motivationmentioning

confidence: 99%

New Routes from Minimal Approximation Error to Principal Components

Miranda

Borgne

Bontempi

2008

Neural Process Lett

104

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Abstract. We introduce two new methods of deriving the classical PCA in the framework of minimizing the mean square error upon performing a lower-dimensional approximation of the data. These methods are based on two forms of the mean square error function. One of the novelties of the presented methods is that the commonly employed process of subtraction of the mean of the data becomes part of the solution of the optimization problem and not a pre-analysis heuristic. We also derive the optimal basis and the minimum error of approximation in this framework and demonstrate the elegance of our solution in comparison with an existing solution in the framework.

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Introduction to Total Least Squares and Errors-In-Variables Modeling

Cited by 32 publications

References 0 publications

An improved strategy for regression of biophysical variables and Landsat ETM+ data

An improved strategy for regression of biophysical variables and Landsat ETM+ data

Untitled

New Routes from Minimal Approximation Error to Principal Components

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