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Discriminant analysis through a semiparametric model

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  • Y. Lin

Abstract

We consider a semiparametric generalisation of normal-theory discriminant analysis. The semiparametric model assumes that, after unspecified univariate monotone transformations, the class distributions are multivariate normal. We introduce an estimation procedure based on the distribution quantiles, in which the parameters of the semiparametric model are estimated directly without estimating the nonparametric transformations. The procedure is computationally fast and the estimation accuracy is shown to have the usual parametric rate. The relationship between the method and more general nonparametric discriminant analysis is discussed. The semiparametric specification of the class densities is a submodel of the nonparametric log density functional analysis of variance model in which the main effects are completely nonparametric but the interaction terms are specified semiparametrically. Simulations and real examples are used to illustrate the procedure. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Y. Lin, 2003. "Discriminant analysis through a semiparametric model," Biometrika, Biometrika Trust, vol. 90(2), pages 379-392, June.
    • Handle: RePEc:oup:biomet:v:90:y:2003:i:2:p:379-392
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    Cited by:

    1. Jiang, Binyan & Leng, Chenlei, 2016. "High dimensional discrimination analysis via a semiparametric model," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 103-110.
    2. Mai, Qing & Zou, Hui, 2015. "Sparse semiparametric discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 175-188.
    3. Debashis Ghosh, 2004. "Semiparametric methods for the binormal model with multiple biomarkers," The University of Michigan Department of Biostatistics Working Paper Series 1046, Berkeley Electronic Press.
    4. Jianqing Fan & Lingzhou Xue & Hui Zou, 2016. "Multitask Quantile Regression Under the Transnormal Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1726-1735, October.
    5. Holly Janes & Margaret S. Pepe, 2008. "Matching in Studies of Classification Accuracy: Implications for Analysis, Efficiency, and Assessment of Incremental Value," Biometrics, The International Biometric Society, vol. 64(1), pages 1-9, March.
    6. Nadja Klein & Torsten Hothorn & Luisa Barbanti & Thomas Kneib, 2022. "Multivariate conditional transformation models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 116-142, March.
    7. Debashis Ghosh, 2004. "Semiparametic models and estimation procedures for binormal ROC curves with multiple biomarkers," The University of Michigan Department of Biostatistics Working Paper Series 1038, Berkeley Electronic Press.

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