Shapiro, Larry S.; Brady, Michael Rejecting outliers and estimating errors in an orthogonal-regression framework. (English) Zbl 0846.62054 Philos. Trans. R. Soc. Lond., Ser. A 350, No. 1694, 407-439 (1995). Summary: Least squares minimization is by nature global and, hence, vulnerable to distortion by outliers. We present a novel technique to reject outliers from an \(m\)-dimensional data set when the underlying model is a hyperplane (a line in two dimensions, a plane in three dimensions). The technique has a sound statistical basis and assumes that Gaussian noise corrupts the otherwise valid data. The majority of alternative techniques available in the literature focuses on ordinary least squares, where a single variable is designated to be dependent on all others – a model that is often unsuitable in practice. The method presented here operates in the more general framework of orthogonal regression, and uses a new regression diagnostic based on eigendecompositions. It subsumes the traditional residuals scheme and, using matrix perturbation theory, provides an error model for the solution once the contaminants have been removed. Cited in 2 Documents MSC: 62J20 Diagnostics, and linear inference and regression 62J05 Linear regression; mixed models 62P99 Applications of statistics 62F35 Robustness and adaptive procedures (parametric inference) Keywords:least squares minimization; robust statistics; hyperplane covariance matrix; computer vision application; affine epipolar geometry; outliers; Gaussian noise; orthogonal regression; eigendecompositions; residuals; matrix perturbation theory Software:alr3 PDFBibTeX XMLCite \textit{L. S. Shapiro} and \textit{M. Brady}, Philos. Trans. R. Soc. Lond., Ser. A 350, No. 1694, 407--439 (1995; Zbl 0846.62054) Full Text: DOI