IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v436y2023ics0096300322005677.html
   My bibliography  Save this article

Geometrically designed variable knot splines in generalized (non-)linear models

Author

Listed:
  • Dimitrova, Dimitrina S.
  • Kaishev, Vladimir K.
  • Lattuada, Andrea
  • Verrall, Richard J.

Abstract

In this paper we extend the GeDS methodology, recently developed by Kaishev et al. [18] for the Normal univariate spline regression case, to the more general GNM/GLM context. Our approach is to view the (non-)linear predictor as a spline with free knots which are estimated, along with the regression coefficients and the degree of the spline, using a two stage algorithm. In stage A, a linear (degree one) free-knot spline is fitted to the data applying iteratively re-weighted least squares. In stage B, a Schoenberg variation diminishing spline approximation to the fit from stage A is constructed, thus simultaneously producing spline fits of second, third and higher degrees. We demonstrate, based on a thorough numerical investigation that the nice properties of the Normal GeDS methodology carry over to its GNM extension and GeDS favourably compares with other existing spline methods.

Suggested Citation

  • Dimitrova, Dimitrina S. & Kaishev, Vladimir K. & Lattuada, Andrea & Verrall, Richard J., 2023. "Geometrically designed variable knot splines in generalized (non-)linear models," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    • Handle: RePEc:eee:apmaco:v:436:y:2023:i:c:s0096300322005677
    DOI: 10.1016/j.amc.2022.127493
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322005677
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127493?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. Gu, Chong, 2014. "Smoothing Spline ANOVA Models: R Package gss," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i05).
    2. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    3. Zhou S. & Shen X., 2001. "Spatially Adaptive Regression Splines and Accurate Knot Selection Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 247-259, March.
    4. Kovács, Péter & Fekete, Andrea M., 2019. "Nonlinear least-squares spline fitting with variable knots," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 490-501.
    5. Yang, Lianqiang & Hong, Yongmiao, 2017. "Adaptive penalized splines for data smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 70-83.
    6. Shen X. & Ye J., 2002. "Adaptive Model Selection," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 210-221, March.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    8. Dimitrova, Dimitrina S. & Kaishev, Vladimir K. & Penev, Spiridon I., 2008. "GeD spline estimation of multivariate Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3570-3582, March.
    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. Papkov, Galen I. & Scott, David W., 2010. "Local-moment nonparametric density estimation of pre-binned data," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3421-3429, December.
    2. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    3. Song Liu & Yuhong Yang, 2012. "Combining models in longitudinal data analysis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 233-254, April.
    4. Binder, Harald & Sauerbrei, Willi, 2008. "Increasing the usefulness of additive spline models by knot removal," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5305-5318, August.
    5. Yang, Lianqiang & Hong, Yongmiao, 2017. "Adaptive penalized splines for data smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 70-83.
    6. Otto-Sobotka, Fabian & Salvati, Nicola & Ranalli, Maria Giovanna & Kneib, Thomas, 2019. "Adaptive semiparametric M-quantile regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 116-129.
    7. Mestekemper, Thomas & Windmann, Michael & Kauermann, Göran, 2010. "Functional hourly forecasting of water temperature," International Journal of Forecasting, Elsevier, vol. 26(4), pages 684-699, October.
    8. Naschold, Felix, 2012. "“The Poor Stay Poor”: Household Asset Poverty Traps in Rural Semi-Arid India," World Development, Elsevier, vol. 40(10), pages 2033-2043.
    9. Arthur Charpentier & Emmanuel Flachaire & Antoine Ly, 2017. "Econom\'etrie et Machine Learning," Papers 1708.06992, arXiv.org, revised Mar 2018.
    10. Hyunju Son & Youyi Fong, 2021. "Fast grid search and bootstrap‐based inference for continuous two‐phase polynomial regression models," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    11. Welham, S.J. & Thompson, R., 2009. "A note on bimodality in the log-likelihood function for penalized spline mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 920-931, February.
    12. Dlugosz, Stephan & Mammen, Enno & Wilke, Ralf A., 2017. "Generalized partially linear regression with misclassified data and an application to labour market transitions," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 145-159.
    13. Longhi, Christian & Musolesi, Antonio & Baumont, Catherine, 2014. "Modeling structural change in the European metropolitan areas during the process of economic integration," Economic Modelling, Elsevier, vol. 37(C), pages 395-407.
    14. Kuhlenkasper, Torben & Kauermann, Göran, 2010. "Female wage profiles: An additive mixed model approach to employment breaks due to childcare," HWWI Research Papers 2-18, Hamburg Institute of International Economics (HWWI).
    15. Strasak, Alexander M. & Umlauf, Nikolaus & Pfeiffer, Ruth M. & Lang, Stefan, 2011. "Comparing penalized splines and fractional polynomials for flexible modelling of the effects of continuous predictor variables," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1540-1551, April.
    16. Christian Schluter & Jackline Wahba, 2012. "Abstract: Illegal Migration, Wages, and Remittances: Semi-Parametric Estimation of Illegality Effects," Norface Discussion Paper Series 2012037, Norface Research Programme on Migration, Department of Economics, University College London.
    17. Zi Ye & Giles Hooker & Stephen P. Ellner, 2021. "Generalized Single Index Models and Jensen Effects on Reproduction and Survival," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 492-512, September.
    18. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    19. Carlo Fezzi & Ian Bateman, 2015. "The Impact of Climate Change on Agriculture: Nonlinear Effects and Aggregation Bias in Ricardian Models of Farmland Values," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 2(1), pages 57-92.
    20. Blöchl, Andreas, 2014. "Trend Estimation with Penalized Splines as Mixed Models for Series with Structural Breaks," Discussion Papers in Economics 18446, University of Munich, Department of Economics.

    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:apmaco:v:436:y:2023:i:c:s0096300322005677. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.