IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v81y2019i2d10.1007_s13571-018-0158-1.html
   My bibliography  Save this article

Wavelet-Based Estimation of Generalized Discriminant Functions

Author

Listed:
  • Michel H. Montoril

    (Federal University of Juiz de Fora)

  • Woojin Chang

    (Seoul National University)

  • Brani Vidakovic

    (Georgia Institute of Technology)

Abstract

In this work we propose a wavelet-based classifier method for binary classification. Basically, based on a training data set, we provide a classifier rule with minimum mean square error. Under mild assumptions, we present asymptotic results that provide the rates of convergence of our method compared to the Bayes classifier, ensuring universal consistency and strong universal consistency. Furthermore, in order to evaluate the performance of the proposed methodology for finite samples, we illustrate the approach using Monte Carlo simulations and real data set applications. The performance of the proposed methodology is compared with other classification methods widely used in the literature: support vector machine and logistic regression model. Numerical results showed a very competitive performance of the new wavelet-based classifier.

Suggested Citation

  • Michel H. Montoril & Woojin Chang & Brani Vidakovic, 2019. "Wavelet-Based Estimation of Generalized Discriminant Functions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 318-349, December.
  • Handle: RePEc:spr:sankhb:v:81:y:2019:i:2:d:10.1007_s13571-018-0158-1
    DOI: 10.1007/s13571-018-0158-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-018-0158-1
    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/s13571-018-0158-1?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. Woojin Chang & Seong‐Hee Kim & Brani Vidakovic, 2003. "Wavelet‐based estimation of a discriminant function," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 19(3), pages 185-198, July.
    2. Jianhua Z. Huang & Haipeng Shen, 2004. "Functional Coefficient Regression Models for Non‐linear Time Series: A Polynomial Spline Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 515-534, December.
    3. Cai, T. Tony & Brown, Lawrence D., 1999. "Wavelet estimation for samples with random uniform design," Statistics & Probability Letters, Elsevier, vol. 42(3), pages 313-321, April.
    4. Olvi L. Mangasarian & W. Nick Street & William H. Wolberg, 1995. "Breast Cancer Diagnosis and Prognosis Via Linear Programming," Operations Research, INFORMS, vol. 43(4), pages 570-577, August.
    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. Michael Wegener & Göran Kauermann, 2017. "Forecasting in nonlinear univariate time series using penalized splines," Statistical Papers, Springer, vol. 58(3), pages 557-576, September.
    2. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    3. Sexton, Randall S. & Dorsey, Robert E. & Johnson, John D., 1999. "Optimization of neural networks: A comparative analysis of the genetic algorithm and simulated annealing," European Journal of Operational Research, Elsevier, vol. 114(3), pages 589-601, May.
    4. Cai Zongwu & Chen Linna & Fang Ying, 2012. "A New Forecasting Model for USD/CNY Exchange Rate," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(3), pages 1-20, September.
    5. Olga Klopp & Marianna Pensky, 2013. "Sparse High-dimensional Varying Coefficient Model : Non-asymptotic Minimax Study," Working Papers 2013-30, Center for Research in Economics and Statistics.
    6. Cizek, Pavel & Koo, Chao, 2017. "Jump-Preserving Varying-Coefficient Models for Nonlinear Time Series," Other publications TiSEM c849e96f-3ad1-461e-96c6-f, Tilburg University, School of Economics and Management.
    7. Qiu, Jia & Li, Degao & You, Jinhong, 2015. "SCAD-penalized regression for varying-coefficient models with autoregressive errors," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 100-118.
    8. Harvill, Jane L. & Ray, Bonnie K., 2005. "A note on multi-step forecasting with functional coefficient autoregressive models," International Journal of Forecasting, Elsevier, vol. 21(4), pages 717-727.
    9. Brandner, Hubertus & Lessmann, Stefan & Voß, Stefan, 2013. "A memetic approach to construct transductive discrete support vector machines," European Journal of Operational Research, Elsevier, vol. 230(3), pages 581-595.
    10. Tang Qingguo & Cheng Longsheng, 2010. "B-spline estimation for spatial data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 197-217.
    11. W. Art Chaovalitwongse & Ya-Ju Fan & Rajesh C. Sachdeo, 2008. "Novel Optimization Models for Abnormal Brain Activity Classification," Operations Research, INFORMS, vol. 56(6), pages 1450-1460, December.
    12. Chesneau, Christophe, 2007. "Regression with random design: A minimax study," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 40-53, January.
    13. Umberto Amato & Anestis Antoniadis & Italia Feis & Irène Gijbels, 2022. "Penalized wavelet estimation and robust denoising for irregular spaced data," Computational Statistics, Springer, vol. 37(4), pages 1621-1651, September.
    14. Tamilselvan, Prasanna & Wang, Pingfeng, 2013. "Failure diagnosis using deep belief learning based health state classification," Reliability Engineering and System Safety, Elsevier, vol. 115(C), pages 124-135.
    15. Yaqiong Cui & Jukka Sirén & Timo Koski & Jukka Corander, 2016. "Simultaneous Predictive Gaussian Classifiers," Journal of Classification, Springer;The Classification Society, vol. 33(1), pages 73-102, April.
    16. Chen, Xiaohong & Christensen, Timothy M., 2015. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," Journal of Econometrics, Elsevier, vol. 188(2), pages 447-465.
    17. repec:wyi:journl:002135 is not listed on IDEAS
    18. Ramazan Ünlü & Petros Xanthopoulos, 2019. "A weighted framework for unsupervised ensemble learning based on internal quality measures," Annals of Operations Research, Springer, vol. 276(1), pages 229-247, May.
    19. Jianbo Li & Minggao Gu & Tao Hu, 2012. "General partially linear varying-coefficient transformation models for ranking data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(7), pages 1475-1488, January.
    20. Luz M. Gómez & Rogério F. Porto & Pedro A. Morettin, 2021. "Nonparametric regression with warped wavelets and strong mixing processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1203-1228, December.
    21. Oleg Shestakov, 2020. "Wavelet Thresholding Risk Estimate for the Model with Random Samples and Correlated Noise," Mathematics, MDPI, vol. 8(3), pages 1-8, March.

    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:sankhb:v:81:y:2019:i:2:d:10.1007_s13571-018-0158-1. 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.