IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v17y2002i4d10.1007_s001800200121.html
   My bibliography  Save this article

Function estimation with locally adaptive dynamic models

Author

Listed:
  • Stefan Lang

    (University of Munich)

  • Eva-Maria Pronk

    (University of Munich)

  • Ludwig Fahrmeir

    (University of Munich)

Abstract

Summary We present a nonparametric Bayesian method for fitting unsmooth and highly oscillating functions, which is based on a locally adaptive hierarchical extension of standard dynamic or state space models. The main idea is to introduce locally varying variances in the state equations and to add a further smoothness prior for this variance function. Estimation is fully Bayesian and carried out by recent MCMC techniques. The whole approach can be understood as an alternative to other nonparametric function estimators, such as local or penalized regression with variable bandwidth or smoothing parameter selection. Performance is illustrated with simulated data, including unsmooth examples constructed for wavelet shrinkage, and by an application to sales data. Although the approach is developed for classical Gaussian nonparametric regression, it can be extended to more complex regression problems.

Suggested Citation

  • Stefan Lang & Eva-Maria Pronk & Ludwig Fahrmeir, 2002. "Function estimation with locally adaptive dynamic models," Computational Statistics, Springer, vol. 17(4), pages 479-499, December.
    • Handle: RePEc:spr:compst:v:17:y:2002:i:4:d:10.1007_s001800200121
    DOI: 10.1007/s001800200121
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s001800200121
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s001800200121?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. Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian inference for generalized additive mixed models based on Markov random field priors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(2), pages 201-220.
    2. D. G. T. Denison & B. K. Mallick & A. F. M. Smith, 1998. "Automatic Bayesian curve fitting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 333-350.
    3. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    4. Carter, C.K. & Kohn, R., "undated". "Markov Chain Monte Carlo in Conditionally Gaussian State Space Models," Statistics Working Paper _003, Australian Graduate School of Management.
    5. Håvard Rue, 2001. "Fast sampling of Gaussian Markov random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 325-338.
    6. Carter, C.K. & Kohn, R., "undated". "Robust Bayesian nonparametric regression," Statistics Working Paper _004, Australian Graduate School of Management.
    7. Leonhard Knorr‐Held, 1999. "Conditional Prior Proposals in Dynamic Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(1), pages 129-144, March.
    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. Yu Yue & Paul Speckman & Dongchu Sun, 2012. "Priors for Bayesian adaptive spline smoothing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 577-613, June.
    2. Harm Jan Boonstra & Jan van den Brakel & Sumonkanti Das, 2021. "Multilevel time series modelling of mobility trends in the Netherlands for small domains," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 985-1007, July.
    3. Heim, S. & Fahrmeir, L. & Eilers, P.H.C. & Marx, B.D., 2007. "3D space-varying coefficient models with application to diffusion tensor imaging," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6212-6228, August.
    4. 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.

    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. 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.
    2. Håvard Rue & Ingelin Steinsland & Sveinung Erland, 2004. "Approximating hidden Gaussian Markov random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 877-892, November.
    3. Yu Yue & Paul Speckman & Dongchu Sun, 2012. "Priors for Bayesian adaptive spline smoothing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 577-613, June.
    4. Riccardo Borgoni & Francesco Billari, 2003. "Bayesian spatial analysis of demographic survey data," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 8(3), pages 61-92.
    5. Congdon, Peter, 2006. "A model for non-parametric spatially varying regression effects," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 422-445, January.
    6. Riccardo Borgoni & Francesco C. Billari, 2002. "Bayesian spatial analysis of demographic survey data: an application to contraceptive use at first sexual intercourse," MPIDR Working Papers WP-2002-048, Max Planck Institute for Demographic Research, Rostock, Germany.
    7. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    8. Schmidt, Paul & Mühlau, Mark & Schmid, Volker, 2017. "Fitting large-scale structured additive regression models using Krylov subspace methods," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 59-75.
    9. McCausland, William J. & Miller, Shirley & Pelletier, Denis, 2011. "Simulation smoothing for state-space models: A computational efficiency analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 199-212, January.
    10. Pena, Daniel & Redondas, Dolores, 2006. "Bayesian curve estimation by model averaging," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 688-709, February.
    11. Powers, Stephanie & Gerlach, Richard & Stamey, James, 2010. "Bayesian variable selection for Poisson regression with underreported responses," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3289-3299, December.
    12. Villani, Mattias & Kohn, Robert & Giordani, Paolo, 2009. "Regression density estimation using smooth adaptive Gaussian mixtures," Journal of Econometrics, Elsevier, vol. 153(2), pages 155-173, December.
    13. M. P. Wand, 2000. "A Comparison of Regression Spline Smoothing Procedures," Computational Statistics, Springer, vol. 15(4), pages 443-462, December.
    14. Smith, Michael & Kohn, Robert, 2000. "Nonparametric seemingly unrelated regression," Journal of Econometrics, Elsevier, vol. 98(2), pages 257-281, October.
    15. Volker Schmid & Leonhard Held, 2004. "Bayesian Extrapolation of Space–Time Trends in Cancer Registry Data," Biometrics, The International Biometric Society, vol. 60(4), pages 1034-1042, December.
    16. Birgit Schrödle & Leonhard Held, 2011. "A primer on disease mapping and ecological regression using $${\texttt{INLA}}$$," Computational Statistics, Springer, vol. 26(2), pages 241-258, June.
    17. Feng Li & Mattias Villani, 2013. "Efficient Bayesian Multivariate Surface Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 706-723, December.
    18. Eklund, Jana & Karlsson, Sune, 2007. "Computational Efficiency in Bayesian Model and Variable Selection," Working Papers 2007:4, Örebro University, School of Business.
    19. Stefanie Kalus & Philipp Sämann & Ludwig Fahrmeir, 2014. "Classification of brain activation via spatial Bayesian variable selection in fMRI regression," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(1), pages 63-83, March.
    20. Wai-Yin Poon & Hai-Bin Wang, 2014. "Multivariate partially linear single-index models: Bayesian analysis," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 755-768, December.

    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:spr:compst:v:17:y:2002:i:4:d:10.1007_s001800200121. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.