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Geometric Interpretation of Errors in Multi-Parametrical Fitting Methods Based on Non-Euclidean Norms

Author

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  • George Livadiotis

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

Abstract

The paper completes the multi-parametrical fitting methods, which are based on metrics induced by the non-Euclidean L q -norms, by deriving the errors of the optimal parameter values. This was achieved using the geometric representation of the residuals sum expanded near its minimum, and the geometric interpretation of the errors. Typical fitting methods are mostly developed based on Euclidean norms, leading to the traditional least–square method. On the other hand, the theory of general fitting methods based on non-Euclidean norms is still under development; the normal equations provide implicitly the optimal values of the fitting parameters, while this paper completes the puzzle by improving understanding the derivations and geometric meaning of the optimal errors.

Suggested Citation

  • George Livadiotis, 2019. "Geometric Interpretation of Errors in Multi-Parametrical Fitting Methods Based on Non-Euclidean Norms," Stats, MDPI, vol. 2(4), pages 1-13, October.
    • Handle: RePEc:gam:jstats:v:2:y:2019:i:4:p:29-438:d:281497
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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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