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A class of logistic-type discriminant functions

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  • Shinto Eguchi

Abstract

In two-group discriminant analysis, the Neyman--Pearson Lemma establishes that the ROC, receiver operating characteristic, curve for an arbitrary linear function is everywhere below the ROC curve for the true likelihood ratio. The weighted area between these two curves can be used as a risk function for finding good discriminant functions. The weight function corresponds to the objective of the analysis, for example to minimise the expected cost of misclassification, or to maximise the area under the ROC. The resulting discriminant functions can be estimated by iteratively reweighted logistic regression. We investigate some asymptotic properties in the 'near-logistic' setting, where we assume the covariates have been chosen such that a linear function gives a reasonable, but not necessarily exact, approximation to the true log likelihood ratio. Some examples are discussed, including a study of medical diagnosis in breast cytology. Copyright Biometrika Trust 2002, Oxford University Press.

Suggested Citation

  • Shinto Eguchi, 2002. "A class of logistic-type discriminant functions," Biometrika, Biometrika Trust, vol. 89(1), pages 1-22, March.
    • Handle: RePEc:oup:biomet:v:89:y:2002:i:1:p:1-22
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    Cited by:

    1. Yingye Zheng & Tianxi Cai & Ziding Feng, 2006. "Application of the Time-Dependent ROC Curves for Prognostic Accuracy with Multiple Biomarkers," Biometrics, The International Biometric Society, vol. 62(1), pages 279-287, March.
    2. Osamu Komori, 2011. "A boosting method for maximization of the area under the ROC curve," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(5), pages 961-979, October.
    3. Nishii, Ryuei & Eguchi, Shinto, 2006. "Image classification based on Markov random field models with Jeffreys divergence," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1997-2008, October.
    4. Margaret Sullivan Pepe & Tianxi Cai & Gary Longton, 2006. "Combining Predictors for Classification Using the Area under the Receiver Operating Characteristic Curve," Biometrics, The International Biometric Society, vol. 62(1), pages 221-229, March.
    5. Kenichi Hayashi, 2018. "Asymptotic comparison of semi-supervised and supervised linear discriminant functions for heteroscedastic normal populations," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(2), pages 315-339, June.
    6. Osamu Komori & Shinto Eguchi & John B. Copas, 2015. "Generalized t-statistic for two-group classification," Biometrics, The International Biometric Society, vol. 71(2), pages 404-416, June.
    7. Eguchi, Shinto & Copas, John, 2006. "Interpreting Kullback-Leibler divergence with the Neyman-Pearson lemma," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 2034-2040, October.
    8. Wei Dai & Ming Yang & Chaolong Wang & Tianxi Cai, 2017. "Sequence robust association test for familial data," Biometrics, The International Biometric Society, vol. 73(3), pages 876-884, September.

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