IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v77y2007i16p1608-1621.html
   My bibliography  Save this article

Penalized wavelet monotone regression

Author

Listed:
  • Antoniadis, Anestis
  • Bigot, Jéremie
  • Gijbels, Irène

Abstract

In this paper we focus on nonparametric estimation of a constrained regression function using penalized wavelet regression techniques. This results into a convex optimization problem under linear constraints. Necessary and sufficient conditions for existence of a unique solution are discussed. The estimator is easily obtained via the dual formulation of the optimization problem. In particular we investigate a penalized wavelet monotone regression estimator. We establish the rate of convergence of this estimator, and illustrate its finite sample performance via a simulation study. We also compare its performance with that of a recently proposed constrained estimator. An illustration to some real data is given.

Suggested Citation

  • Antoniadis, Anestis & Bigot, Jéremie & Gijbels, Irène, 2007. "Penalized wavelet monotone regression," Statistics & Probability Letters, Elsevier, vol. 77(16), pages 1608-1621, October.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:16:p:1608-1621
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(07)00136-8
    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. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
    2. E. Mammen & C. Thomas‐Agnan, 1999. "Smoothing Splines and Shape Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 239-252, June.
    3. Antoniadis, A. & Grégoire, G. & Vial, P., 1997. "Random design wavelet curve smoothing," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 225-232, October.
    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. Pang Du & Christopher F. Parmeter & Jeffrey S. Racine, 2012. "Nonparametric Kernel Regression with Multiple Predictors and Multiple Shape Constraints," Department of Economics Working Papers 2012-08, McMaster University.
    2. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
    3. Marco Gallegati, 2019. "A system for dating long wave phases in economic development," Journal of Evolutionary Economics, Springer, vol. 29(3), pages 803-822, July.
    4. Kari Harju & Syed Mujahid Hussain, 2011. "Intraday Seasonalities and Macroeconomic News Announcements," European Financial Management, European Financial Management Association, vol. 17(2), pages 367-390, March.
    5. Mohsen Bahmani-Oskooee & Tsangyao Chang & Zahra (Mila) Elmi & Omid Ranjbar, 2018. "Re-testing Prebisch–Singer hypothesis: new evidence using Fourier quantile unit root test," Applied Economics, Taylor & Francis Journals, vol. 50(4), pages 441-454, January.
    6. Barnett, William A. & Serletis, Apostolos, 2008. "The Differential Approach to Demand Analysis and the Rotterdam Model," MPRA Paper 12319, University Library of Munich, Germany.
    7. Williams, Jonathan, 2004. "Determining management behaviour in European banking," Journal of Banking & Finance, Elsevier, vol. 28(10), pages 2427-2460, October.
    8. Fleissig, Adrian & Swofford, James L., 1996. "A dynamic asymptotically ideal model of money demand," Journal of Monetary Economics, Elsevier, vol. 37(2-3), pages 371-380, April.
    9. Eduardo L. Montoya & Wendy Meiring, 2016. "An F-type test for detecting departure from monotonicity in a functional linear model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 322-337, June.
    10. Naimoli, Antonio & Storti, Giuseppe, 2019. "Heterogeneous component multiplicative error models for forecasting trading volumes," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1332-1355.
    11. Leora Friedberg & Steven Stern, 2014. "Marriage, Divorce, And Asymmetric Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(4), pages 1155-1199, November.
    12. Zhenkai Yang & Mei-Chih Wang & Tsangyao Chang & Wing-Keung Wong & Fangjhy Li, 2022. "Which Factors Determine CO 2 Emissions in China? Trade Openness, Financial Development, Coal Consumption, Economic Growth or Urbanization: Quantile Granger Causality Test," Energies, MDPI, vol. 15(7), pages 1-18, March.
    13. Tue Gørgens & Allan Würtz, 2012. "Testing a parametric function against a non‐parametric alternative in IV and GMM settings," Econometrics Journal, Royal Economic Society, vol. 15(3), pages 462-489, October.
    14. Uctum, Remzi & Renou-Maissant, Patricia & Prat, Georges & Lecarpentier-Moyal, Sylvie, 2017. "Persistence of announcement effects on the intraday volatility of stock returns: Evidence from individual data," Review of Financial Economics, Elsevier, vol. 35(C), pages 43-56.
    15. Atanu Ghoshray & Yurena Mendoza & Mercedes Monfort & Javier Ordoñez, 2018. "Re-assessing causality between energy consumption and economic growth," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-15, November.
    16. Piyu Yue, 1991. "A microeconomic approach to estimating demand: the asymptotically ideal model," Review, Federal Reserve Bank of St. Louis, issue Nov, pages 36-51.
    17. Claudio, Morana & Giacomo, Sbrana, 2017. "Some Financial Implications of Global Warming: An Empirical Assessment," Working Papers 377, University of Milano-Bicocca, Department of Economics, revised 25 Dec 2017.
    18. Claudio, Morana & Giacomo, Sbrana, 2017. "Temperature anomalies, radiative forcing and ENSO," Working Papers 361, University of Milano-Bicocca, Department of Economics, revised 10 Feb 2017.
    19. Lutho Mbekeni & Andrew Phiri, 2019. "Can the South African Reserve Bank (SARB) protect the purchasing power of citizens? A new look at Fisher’s hypothesis," Working Papers 1906, Department of Economics, Nelson Mandela University, revised Sep 2019.
    20. Chen, Shyh-Wei & Xie, Zixiong, 2017. "Asymmetric adjustment and smooth breaks in dividend yields: Evidence from international stock markets," International Review of Economics & Finance, Elsevier, vol. 48(C), pages 339-354.

    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:stapro:v:77:y:2007:i:16:p:1608-1621. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.