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General Fitting Methods Based on L q Norms and their Optimization

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  • George Livadiotis

    (Southwest Research Institute, Space Science & Engineering, San Antonio, TX 78238, USA)

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.

Suggested Citation

  • George Livadiotis, 2020. "General Fitting Methods Based on L q Norms and their Optimization," Stats, MDPI, vol. 3(1), pages 1-16, January.
    • Handle: RePEc:gam:jstats:v:3:y:2020:i:1:p:2-31:d:305710
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    References listed on IDEAS

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    1. Livadiotis, George, 2008. "Approach to block entropy modeling and optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2471-2494.
    2. Livadiotis, George & Moussas, Xenophon, 2007. "The sunspot as an autonomous dynamical system: A model for the growth and decay phases of sunspots," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 436-458.
    3. George Livadiotis, 2019. "Linear Regression with Optimal Rotation," Stats, MDPI, vol. 2(4), pages 1-10, September.
    4. Livadiotis, George, 2007. "Approach to general methods for fitting and their sensitivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 518-536.
    5. Livadiotis, George, 2016. "Non-Euclidean-normed Statistical Mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 240-255.
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