IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v53y2009i7p2550-2562.html
   My bibliography  Save this article

Generalized profiling estimation for global and adaptive penalized spline smoothing

Author

Listed:
  • Cao, Jiguo
  • Ramsay, James O.

Abstract

We propose the generalized profiling method to estimate the multiple regression functions in the framework of penalized spline smoothing, where the regression functions and the smoothing parameter are estimated in two nested levels of optimization. The corresponding gradients and Hessian matrices are worked out analytically, using the Implicit Function Theorem if necessary, which leads to fast and stable computation. Our main contribution is developing the modified delta method to estimate the variances of the regression functions, which include the uncertainty of the smoothing parameter estimates. We further develop adaptive penalized spline smoothing to estimate spatially heterogeneous regression functions, where the smoothing parameter is a function that changes along with the curvature of regression functions. The simulations and application show that the generalized profiling method leads to good estimates for the regression functions and their variances.

Suggested Citation

  • Cao, Jiguo & Ramsay, James O., 2009. "Generalized profiling estimation for global and adaptive penalized spline smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2550-2562, May.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:7:p:2550-2562
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00569-0
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. Vicente Núñez-Antón & Juan Rodríguez-Póo & Philippe Vieu, 1999. "Longitudinal data with nonstationary errors: a nonparametric three-stage approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 201-231, June.
    2. Jiguo Cao & James Ramsay, 2007. "Parameter cascades and profiling in functional data analysis," Computational Statistics, Springer, vol. 22(3), pages 335-351, September.
    3. J. O. Ramsay & G. Hooker & D. Campbell & J. Cao, 2007. "Parameter estimation for differential equations: a generalized smoothing approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 741-796, November.
    4. M. P. Wand, 2000. "A Comparison of Regression Spline Smoothing Procedures," Computational Statistics, Springer, vol. 15(4), pages 443-462, December.
    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. Christian Genest & Johanna G. Nešlehová, 2014. "A Conversation with James O. Ramsay," International Statistical Review, International Statistical Institute, vol. 82(2), pages 161-183, August.
    2. González-Rodríguez, Gil & Colubi, Ana & Gil, María Ángeles, 2012. "Fuzzy data treated as functional data: A one-way ANOVA test approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 943-955.
    3. Bernardi, Mara S. & Carey, Michelle & Ramsay, James O. & Sangalli, Laura M., 2018. "Modeling spatial anisotropy via regression with partial differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 15-30.

    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. Christian Genest & Johanna G. Nešlehová, 2014. "A Conversation with James O. Ramsay," International Statistical Review, International Statistical Institute, vol. 82(2), pages 161-183, August.
    2. Jiguo Cao & Gregor F. Fussmann & James O. Ramsay, 2008. "Estimating a Predator‐Prey Dynamical Model with the Parameter Cascades Method," Biometrics, The International Biometric Society, vol. 64(3), pages 959-967, September.
    3. Carey, Michelle & Gath, Eugene G. & Hayes, Kevin, 2014. "Frontiers in financial dynamics," Research in International Business and Finance, Elsevier, vol. 30(C), pages 369-376.
    4. Bernardi, Mara S. & Carey, Michelle & Ramsay, James O. & Sangalli, Laura M., 2018. "Modeling spatial anisotropy via regression with partial differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 15-30.
    5. Zhou, Jie, 2015. "Detection of influential measurement for ordinary differential equation with application to HIV dynamics," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 324-332.
    6. Carey, M. & Ramsay, J.O., 2021. "Fast stable parameter estimation for linear dynamical systems," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    7. Xinyu Zhang & Jiguo Cao & Raymond J. Carroll, 2017. "Estimating varying coefficients for partial differential equation models," Biometrics, The International Biometric Society, vol. 73(3), pages 949-959, September.
    8. Nanshan, Muye & Zhang, Nan & Xun, Xiaolei & Cao, Jiguo, 2022. "Dynamical modeling for non-Gaussian data with high-dimensional sparse ordinary differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    9. Baisen Liu & Liangliang Wang & Yunlong Nie & Jiguo Cao, 2021. "Semiparametric Mixed-Effects Ordinary Differential Equation Models with Heavy-Tailed Distributions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 428-445, September.
    10. Qianwen Tan & Subhashis Ghosal, 2021. "Bayesian Analysis of Mixed-effect Regression Models Driven by Ordinary Differential Equations," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 3-29, May.
    11. Jaeger, Jonathan & Lambert, Philippe, 2012. "Bayesian penalized smoothing approaches in models specified using affine differential equations with unknown error distributions," LIDAM Discussion Papers ISBA 2012017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Hooker, Giles & Ramsay, James O. & Xiao, Luo, 2016. "CollocInfer: Collocation Inference in Differential Equation Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 75(i02).
    13. Yaeji Lim & Hee-Seok Oh & Ying Kuen Cheung, 2019. "Multiscale Clustering for Functional Data," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 368-391, July.
    14. Ciprian Crainiceanu & David Ruppert & Raymond Carroll, 2004. "Spatially Adaptive Bayesian P-Splines with Heteroscedastic Errors," Johns Hopkins University Dept. of Biostatistics Working Paper Series 1061, Berkeley Electronic Press.
    15. Gianluca Frasso & Jonathan Jaeger & Philippe Lambert, 2016. "Parameter estimation and inference in dynamic systems described by linear partial differential equations," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 259-287, July.
    16. Carlos E. Melo & Oscar O. Melo & Jorge Mateu, 2018. "A distance-based model for spatial prediction using radial basis functions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 263-288, April.
    17. Charu Sharma & Amber Habib & Sunil Bowry, 2018. "Cluster analysis of stocks using price movements of high frequency data from National Stock Exchange," Papers 1803.09514, arXiv.org.
    18. Pascal Deboeck & Steven Boker, 2010. "Modeling Noisy Data with Differential Equations Using Observed and Expected Matrices," Psychometrika, Springer;The Psychometric Society, vol. 75(3), pages 420-437, September.
    19. Yucong Lin & Jinhua Su & Yang Liu & Jue Hou & Feifei Wang, 2024. "Implicit profiling estimation for semiparametric models with bundled parameters," Statistical Papers, Springer, vol. 65(5), pages 3203-3234, July.
    20. Xinyu Zhang & Jiguo Cao & Raymond J. Carroll, 2015. "On the selection of ordinary differential equation models with application to predator-prey dynamical models," Biometrics, The International Biometric Society, vol. 71(1), pages 131-138, March.

    More about this item

    Statistics

    Access and download statistics

    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:53:y:2009:i:7:p:2550-2562. 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.