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Biometrika 2006 93(4):961-972; doi:10.1093/biomet/93.4.961
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© 2006 Biometrika Trust

Isotonic logistic discrimination

Sungyoung Auh1 and Allan R. Sampson2

1 National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, Maryland 20892, U.S.A. auhs{at}ninds.nih.gov, 2 Department of Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A. asampson{at}stat.pitt.edu


  Abstract

We propose an isotonic logistic discrimination procedure which generalises linear logistic discrimination by allowing linear boundaries to be more flexibly shaped as monotone functions of the discriminant variables. Under each of three familiar sampling schemes for obtaining a training dataset, namely prospective, mixture and retrospective, we provide the corresponding likelihood-based inference. An application to a cancer study is given. In addition, we consider theoretical comparisons of our method with two recent algorithmic monotone discrimination procedures.

Key Words: Bayes rule; Isotonic discrimination; Isotonic regression; Logistic discrimination.

Received October 2004. Revised April 2006.


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