IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v71y2014icp654-666.html
   My bibliography  Save this article

Hypercube estimators: Penalized least squares, submodel selection, and numerical stability

Author

Listed:
  • Beran, Rudolf

Abstract

Hypercube estimators for the mean vector in a general linear model include algebraic equivalents to penalized least squares estimators with quadratic penalties and to submodel least squares estimators. Penalized least squares estimators necessarily break down numerically for certain penalty matrices. Equivalent hypercube estimators resist this source of numerical instability. Under conditions, adaptation over a class of candidate hypercube estimators, so as to minimize the estimated quadratic risk, also minimizes the asymptotic risk under the general linear model. Numerical stability of hypercube estimators assists trustworthy adaptation. Hypercube estimators have broad applicability to any statistical methodology that involves penalized least squares. Notably, they extend to general designs the risk reduction achieved by Stein’s multiple shrinkage estimators for balanced observations on an array of means.

Suggested Citation

  • Beran, Rudolf, 2014. "Hypercube estimators: Penalized least squares, submodel selection, and numerical stability," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 654-666.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:654-666
    DOI: 10.1016/j.csda.2013.05.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947313002077
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2013.05.020?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. S. N. Wood, 2000. "Modelling and smoothing parameter estimation with multiple quadratic penalties," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 413-428.
    2. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
    3. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, September.
    4. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, September.
    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. 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.
    2. 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.
    3. Morteza Amini & Mahdi Roozbeh & Nur Anisah Mohamed, 2024. "Separation of the Linear and Nonlinear Covariates in the Sparse Semi-Parametric Regression Model in the Presence of Outliers," Mathematics, MDPI, vol. 12(2), pages 1-17, January.
    4. Philip T. Reiss & R. Todd Ogden, 2010. "Functional Generalized Linear Models with Images as Predictors," Biometrics, The International Biometric Society, vol. 66(1), pages 61-69, March.
    5. Sylvie Charlot & Riccardo Crescenzi & Antonio Musolesi, 2014. "Augmented and Unconstrained: revisiting the Regional Knowledge Production Function," SEEDS Working Papers 2414, SEEDS, Sustainability Environmental Economics and Dynamics Studies, revised Aug 2014.
    6. Simon N. Wood, 2020. "Inference and computation with generalized additive models and their extensions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 307-339, June.
    7. Silvia Ferrini & Carlo Fezzi, 2012. "Generalized Additive Models for Nonmarket Valuation via Revealed or Stated Preference Methods," Land Economics, University of Wisconsin Press, vol. 88(4), pages 782-802.
    8. Musolesi Antonio & Mazzanti Massimiliano, 2014. "Nonlinearity, heterogeneity and unobserved effects in the carbon dioxide emissions-economic development relation for advanced countries," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(5), pages 521-541, December.
    9. Greiner, Alfred & Kauermann, Göran, 2008. "Debt policy in euro area countries: Evidence for Germany and Italy using penalized spline smoothing," Economic Modelling, Elsevier, vol. 25(6), pages 1144-1154, November.
    10. Baccini, Michela & Biggeri, Annibale & Lagazio, Corrado & Lertxundi, Aitana & Saez, Marc, 2007. "Parametric and semi-parametric approaches in the analysis of short-term effects of air pollution on health," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4324-4336, May.
    11. Maik Eisenbeiss & Goran Kauermann & Willi Semmler, 2007. "Estimating Beta-Coefficients of German Stock Data: A Non-Parametric Approach," The European Journal of Finance, Taylor & Francis Journals, vol. 13(6), pages 503-522.
    12. Takuma Yoshida, 2016. "Asymptotics and smoothing parameter selection for penalized spline regression with various loss functions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(4), pages 278-303, November.
    13. Gerhard Tutz & Margret-Ruth Oelker, 2017. "Modelling Clustered Heterogeneity: Fixed Effects, Random Effects and Mixtures," International Statistical Review, International Statistical Institute, vol. 85(2), pages 204-227, August.
    14. Benjamin Owusu & Bettina Bökemeier & Alfred Greiner, 2023. "Assessing nonlinearities and heterogeneity in debt sustainability analysis: a panel spline approach," Empirical Economics, Springer, vol. 64(3), pages 1315-1346, March.
    15. Massimiliano Mazzanti & Antonio Musolesi, 2013. "Nonlinearity, Heterogeneity and Unobserved Effects in the CO2-income Relation for Advanced Countries," Working Papers 2013.91, Fondazione Eni Enrico Mattei.
    16. Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.
    17. Simon N. Wood & Natalya Pya & Benjamin Säfken, 2016. "Smoothing Parameter and Model Selection for General Smooth Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1548-1563, October.
    18. Belitz, Christiane & Lang, Stefan, 2008. "Simultaneous selection of variables and smoothing parameters in structured additive regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 61-81, September.
    19. Greiner, Alfred & Kauermann, Goran, 2007. "Sustainability of US public debt: Estimating smoothing spline regressions," Economic Modelling, Elsevier, vol. 24(2), pages 350-364, March.
    20. Bettina Fincke & Alfred Greiner, 2012. "How to assess debt sustainability? Some theory and empirical evidence for selected euro area countries," Applied Economics, Taylor & Francis Journals, vol. 44(28), pages 3717-3724, October.

    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:csdana:v:71:y:2014:i:c:p:654-666. 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.elsevier.com/locate/csda .

    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.