General Fitting Methods Based on L q Norms and their Optimization

George Livadiotis
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George Livadiotis: Southwest Research Institute, Space Science & Engineering, San Antonio, TX 78238, USA

Stats, 2020, vol. 3, issue 1, 1-16

Abstract: The widely used fitting method of least squares is neither unique nor does it provide the most accurate results. Other fitting methods exist which differ on the metric norm can be used for expressing the total deviations between the given data and the fitted statistical model. The least square method is based on the Euclidean norm L 2 , while the alternative least absolute deviations method is based on the Taxicab norm, L 1 . In general, there is an infinite number of fitting methods based on metric spaces induced by L q norms. The most accurate, and thus optimal method, is the one with the (i) highest sensitivity, given by the curvature at the minimum of total deviations, (ii) the smallest errors of the fitting parameters, (iii) best goodness of fitting. The first two cases concern fitting methods where the given curve functions or datasets do not have any errors, while the third case deals with fitting methods where the given data are assigned with errors.

Keywords: fitting; regression; non-Euclidean norms (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2020
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