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Wavelet-Based Estimation of Generalized Discriminant Functions

Author

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
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