IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v375y2007i2p518-536.html
   My bibliography  Save this article

Approach to general methods for fitting and their sensitivity

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437106010314
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2006.09.027?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. George Livadiotis, 2019. "Linear Regression with Optimal Rotation," Stats, MDPI, vol. 2(4), pages 1-10, September.
    3. George Livadiotis, 2018. "Complex Symmetric Formulation of Maxwell Equations for Fields and Potentials," Mathematics, MDPI, vol. 6(7), pages 1-10, July.
    4. 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.
    5. George Livadiotis, 2020. "General Fitting Methods Based on L q Norms and their Optimization," Stats, MDPI, vol. 3(1), pages 1-16, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dunn, Sarah & Wilkinson, Sean M., 2016. "Increasing the resilience of air traffic networks using a network graph theory approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 90(C), pages 39-50.
    2. Sean Wilkinson & Sarah Dunn & Shu Ma, 2012. "The vulnerability of the European air traffic network to spatial hazards," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 60(3), pages 1027-1036, February.
    3. Wang, Qiuping A., 2021. "Principle of least effort vs. maximum efficiency: deriving Zipf-Pareto's laws," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:375:y:2007:i:2:p:518-536. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.