IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i9p1600-d414835.html
   My bibliography  Save this article

Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh Support

Author

Listed:
  • Francisco José Navarro-González

    (Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain)

  • Yolanda Villacampa

    (Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain)

  • Mónica Cortés-Molina

    (Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain)

  • Salvador Ivorra

    (Department of Civil Engineering, University of Alicante, 03690 Alicante, Spain)

Abstract

Estimation problems are frequent in several fields such as engineering, economics, and physics, etc. Linear and non-linear regression are powerful techniques based on optimizing an error defined over a dataset. Although they have a strong theoretical background, the need of supposing an analytical expression sometimes makes them impractical. Consequently, a group of other approaches and methodologies are available, from neural networks to random forest, etc. This work presents a new methodology to increase the number of available numerical techniques and corresponds to a natural evolution of the previous algorithms for regression based on finite elements developed by the authors improving the computational behavior and allowing the study of problems with a greater number of points. It possesses an interesting characteristic: Its direct and clear geometrical meaning. The modelling problem is presented from the point of view of the statistical analysis of the data noise considered as a random field. The goodness of fit of the generated models has been tested and compared with some other methodologies validating the results with some experimental campaigns obtained from bibliography in the engineering field, showing good approximation. In addition, a small variation on the data estimation algorithm allows studying overfitting in a model, that it is a problematic fact when numerical methods are used to model experimental values.

Suggested Citation

  • Francisco José Navarro-González & Yolanda Villacampa & Mónica Cortés-Molina & Salvador Ivorra, 2020. "Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh Support," Mathematics, MDPI, vol. 8(9), pages 1-27, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1600-:d:414835
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/9/1600/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/9/1600/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mohamed Machkouri, 2007. "Nonparametric Regression Estimation for Random Fields in a Fixed-Design," Statistical Inference for Stochastic Processes, Springer, vol. 10(1), pages 29-47, January.
    2. Oliveira, Victor De, 2000. "Bayesian prediction of clipped Gaussian random fields," Computational Statistics & Data Analysis, Elsevier, vol. 34(3), pages 299-314, September.
    3. Marc Hallin & Zudi Lu & Lanh T. Tran, 2004. "Local linear spatial regression," ULB Institutional Repository 2013/2131, ULB -- Universite Libre de Bruxelles.
    Full references (including those not matched with items on IDEAS)

    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. Peligrad, Magda & Sang, Hailin & Xiao, Yimin & Yang, Guangyu, 2022. "Limit theorems for linear random fields with innovations in the domain of attraction of a stable law," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 596-621.
    2. El Machkouri, Mohamed & Es-Sebaiy, Khalifa & Ouassou, Idir, 2017. "On local linear regression for strongly mixing random fields," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 103-115.
    3. Tang Qingguo, 2015. "Robust estimation for spatial semiparametric varying coefficient partially linear regression," Statistical Papers, Springer, vol. 56(4), pages 1137-1161, November.
    4. Gao, Jiti & Lu, Zudi & Tjostheim, Dag, 2003. "Estimation in semiparametric spatial regression," MPRA Paper 11979, University Library of Munich, Germany, revised Jul 2005.
    5. Hongxia Wang & Xiao Jin & Jianian Wang & Hongxia Hao, 2023. "Nonparametric Estimation for High-Dimensional Space Models Based on a Deep Neural Network," Mathematics, MDPI, vol. 11(18), pages 1-37, September.
    6. Hongxia Wang & Jinde Wang & Bo Huang, 2012. "Prediction for spatio-temporal models with autoregression in errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 217-244.
    7. repec:esx:essedp:767 is not listed on IDEAS
    8. Tang Qingguo & Cheng Longsheng, 2010. "B-spline estimation for spatial data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 197-217.
    9. Solaiman Afroughi & Soghrat Faghihzadeh & Majid Jafari Khaledi & Mehdi Ghandehari Motlagh & Ebrahim Hajizadeh, 2011. "Analysis of clustered spatially correlated binary data using autologistic model and Bayesian method with an application to dental caries of 3--5-year-old children," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2763-2774, February.
    10. Liangjun Su & Xi Qu, 2017. "Specification Test for Spatial Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 572-584, October.
    11. Gérard Biau & Benoît Cadre, 2004. "Nonparametric Spatial Prediction," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 327-349, October.
    12. Kuangyu Wen & Ximing Wu & David J. Leatham, 2021. "Spatially Smoothed Kernel Densities with Application to Crop Yield Distributions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 349-366, September.
    13. Jenish, Nazgul, 2012. "Nonparametric spatial regression under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 167(1), pages 224-239.
    14. Higgs, Megan Dailey & Hoeting, Jennifer A., 2010. "A clipped latent variable model for spatially correlated ordered categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1999-2011, August.
    15. Bastian Schäfer, 2021. "Bandwidth selection for the Local Polynomial Double Conditional Smoothing under Spatial ARMA Errors," Working Papers CIE 146, Paderborn University, CIE Center for International Economics.
    16. Frédérick Demers & David Dupuis, 2005. "Forecasting Canadian GDP: Region-Specific versus Countrywide Information," Staff Working Papers 05-31, Bank of Canada.
    17. Victor De Oliveira, 2017. "Geostatistical Binary Data: Models, Properties And Connections," Working Papers 0151mss, College of Business, University of Texas at San Antonio.
    18. Mohamed El Machkouri, 2011. "Asymptotic normality of the Parzen–Rosenblatt density estimator for strongly mixing random fields," Statistical Inference for Stochastic Processes, Springer, vol. 14(1), pages 73-84, February.
    19. Hongxia Wang & Jinde Wang, 2009. "Estimation of the trend function for spatio-temporal models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 567-588.
    20. Pierrette Chagneau & Frédéric Mortier & Nicolas Picard & Jean-Noël Bacro, 2011. "A Hierarchical Bayesian Model for Spatial Prediction of Multivariate Non-Gaussian Random Fields," Biometrics, The International Biometric Society, vol. 67(1), pages 97-105, March.
    21. Benhenni, Karim & Su, Yingcai, 2016. "Optimal sampling designs for nonparametric estimation of spatial averages of random fields," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 341-351.

    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:gam:jmathe:v:8:y:2020:i:9:p:1600-:d:414835. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.