IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v75y2014icp142-150.html
   My bibliography  Save this article

A frame based shrinkage procedure for fast oscillating functions

Author

Listed:
  • De Canditiis, Daniela

Abstract

In non-parametric regression analysis the advantage of frames with respect to classical orthonormal bases is that they can furnish an efficient representation of a more broad class of functions. For example, fast oscillating functions as audio, speech, sonar, radar, EEG and stock market are much more well represented by a frame, with similar oscillating characteristic, than by a classical orthonormal basis. In this respect, a new frame based shrinkage estimator is derived as the Empirical Regularized version of the optimal Shrinkage estimator generalized to the frame operator. An analytic expression of it is furnished leading to an efficient implementation. Results on standard and real test functions are shown.

Suggested Citation

  • De Canditiis, Daniela, 2014. "A frame based shrinkage procedure for fast oscillating functions," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 142-150.
    • Handle: RePEc:eee:csdana:v:75:y:2014:i:c:p:142-150
    DOI: 10.1016/j.csda.2014.01.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947314000279
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2014.01.016?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. Antoniadis, Anestis & Bigot, Jeremie & Sapatinas, Theofanis, 2001. "Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 6(i06).
    2. Patrick J. Wolfe & Simon J. Godsill & Wee‐Jing Ng, 2004. "Bayesian variable selection and regularization for time–frequency surface estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 575-589, August.
    3. Hotz, Thomas & Marnitz, Philipp & Stichtenoth, Rahel & Davies, Laurie & Kabluchko, Zakhar & Munk, Axel, 2012. "Locally adaptive image denoising by a statistical multiresolution criterion," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 543-558.
    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. De Canditiis, D. & Pensky, M. & Wolfe, P.J., 2018. "Denoising strategies for general finite frames," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 147(C), pages 90-99.

    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. Bin Jiang & Anastasios Panagiotelis & George Athanasopoulos & Rob Hyndman & Farshid Vahid, 2016. "Bayesian Rank Selection in Multivariate Regression," Monash Econometrics and Business Statistics Working Papers 6/16, Monash University, Department of Econometrics and Business Statistics.
    2. Autin, Florent & Freyermuth, Jean-Marc & von Sachs, Rainer, 2011. "Combining thresholding rules: a new way to improve the performance of wavelet estimators," LIDAM Discussion Papers ISBA 2011021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Yu, Dengdeng & Zhang, Li & Mizera, Ivan & Jiang, Bei & Kong, Linglong, 2019. "Sparse wavelet estimation in quantile regression with multiple functional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 12-29.
    4. Guy P. Nason & Ben Powell & Duncan Elliott & Paul A. Smith, 2017. "Should we sample a time series more frequently?: decision support via multirate spectrum estimation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(2), pages 353-407, February.
    5. Nilotpal Sanyal & Marco A. R. Ferreira, 2017. "Bayesian Wavelet Analysis Using Nonlocal Priors with an Application to fMRI Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 361-388, November.
    6. T. Palanisamy & J. Ravichandran, 2015. "A wavelet-based hybrid approach to estimate variance function in heteroscedastic regression models," Statistical Papers, Springer, vol. 56(3), pages 911-932, August.
    7. Florent Autin & Jean-Marc Freyermuth & Rainer Von Sachs, 2014. "Block-threshold-adapted Estimators via a Maxiset Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 240-258, March.
    8. Vincent Rivoirard, 2004. "Thresholding procedure with priors based on Pareto distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 213-246, June.
    9. Autin, Florent & Freyermuth, Jean-Marc & von Sachs, Rainer, 2011. "Block-Threshold-Adapted Estimators via a maxiset approach," LIDAM Discussion Papers ISBA 2011017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Helida Nurcahayani & I Nyoman Budiantara & Ismaini Zain, 2021. "The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression," Mathematics, MDPI, vol. 9(10), pages 1-22, May.
    11. Serban, Nicoleta, 2010. "Noise reduction for enhanced component identification in multi-dimensional biomolecular NMR studies," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1051-1065, April.
    12. Aminghafari, Mina & Cheze, Nathalie & Poggi, Jean-Michel, 2006. "Multivariate denoising using wavelets and principal component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2381-2398, May.
    13. De Canditiis, D. & Pensky, M. & Wolfe, P.J., 2018. "Denoising strategies for general finite frames," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 147(C), pages 90-99.
    14. Fryzlewicz, Piotr, 2007. "Bivariate hard thresholding in wavelet function estimation," LSE Research Online Documents on Economics 25219, London School of Economics and Political Science, LSE Library.
    15. Fabien Navarro & Adrien Saumard, 2017. "Slope heuristics and V-Fold model selection in heteroscedastic regression using strongly localized bases," Working Papers 2017-67, Center for Research in Economics and Statistics.
    16. T. W. Randolph & Y. Yasui, 2006. "Multiscale Processing of Mass Spectrometry Data," Biometrics, The International Biometric Society, vol. 62(2), pages 589-597, June.
    17. Beknazaryan, Aleksandr & Sang, Hailin, 2022. "Nonparametric regression with modified ReLU networks," Statistics & Probability Letters, Elsevier, vol. 190(C).
    18. Autin, F. & Freyermuth, Jean-Marc & von Sachs, Rainer, 2011. "Ideal denoising within a family of tree-structured wavelet estimators," LIDAM Discussion Papers ISBA 2011002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Youssef Taleb & Edward A. K. Cohen, 2021. "Multiresolution analysis of point processes and statistical thresholding for Haar wavelet-based intensity estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(2), pages 395-423, April.
    20. Jacinta Chan Phooi M’ng & Mohammadali Mehralizadeh, 2016. "Forecasting East Asian Indices Futures via a Novel Hybrid of Wavelet-PCA Denoising and Artificial Neural Network Models," PLOS ONE, Public Library of Science, vol. 11(6), pages 1-29, June.

    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:75:y:2014:i:c:p:142-150. 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.