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Approach to general methods for fitting and their sensitivity

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  • Livadiotis, George

Abstract

This paper examines the performance of various fitting methods between the curves of two explicit functions. The approximating test function is considered to be one-parametrical first and multi-parametrical directly after. The widely used least square deviations constitutional method based on the Euclidean norm is not unique. Methods based on q-norm, for q⩾1, can also be defined. Emphasis on these methods, especially for q=1, is placed. Furthermore, any functional Φ fulfilling the norm's preconditions induces a metric for deviations, supporting a respective method for fitting through the minimization of total deviations. This dissertation addresses also the sensitivity of each method that is a measure of how abrupt the variation of the total deviations near its minimum is. We show that the least square method does not indispensably perform the largest sensitivity in regard to the alternative methods based on other q-norms. In addition, we represent the explicit general expression of normal equations, from which the fitting can be achieved, and the sensitivity, from which one can positively extract the suitable norm for a given model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:375:y:2007:i:2:p:518-536
    DOI: 10.1016/j.physa.2006.09.027
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    References listed on IDEAS

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    1. Li, W. & Wang, Q.A. & Nivanen, L. & Le Méhauté, A., 2006. "How to fit the degree distribution of the air network?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 262-272.
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    Cited by:

    1. 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.
    2. Wolf-Dieter Richter, 2016. "Exact inference on scaling parameters in norm and antinorm contoured sample distributions," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-16, December.
    3. George Livadiotis, 2019. "Linear Regression with Optimal Rotation," Stats, MDPI, vol. 2(4), pages 1-10, September.
    4. George Livadiotis, 2020. "General Fitting Methods Based on L q Norms and their Optimization," Stats, MDPI, vol. 3(1), pages 1-16, January.
    5. George Livadiotis, 2018. "Complex Symmetric Formulation of Maxwell Equations for Fields and Potentials," Mathematics, MDPI, vol. 6(7), pages 1-10, July.

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