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The Generalized Receiver Operating Characteristic Curve

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  • Heikki Kauppi

    (University of Turku)

Abstract

The problem is to predict whether a random outcome is a "success" (R=1) or a "failure" (R=0) given a continuous variable Z. The performance of a prediction rule $D=D(Z)\in \{1,0\}$ boils down to two probabilities, beta =Pr (D=1|R=1) and alpha =Pr (D=1|R=0). We wish beta is high, alpha is low. Given a set of rules D such that any d in D is attributed to a specific alpha, I define the "generalized" receiver operating characteristic (GROC) curve as a function that returns beta for any alpha in (0,1]. The GROC curve associated with D ={d(Z)=I(Z>c),c in R} is the "conventional" ROC curve, while an "efficient" ROC (EROC) curve derives from rules that return the largest possible beta for any alpha in (0,1]. I present estimation theory for the GROC curve and develop procedures for estimating the efficient rules and the associated EROC curve under semiparametric and nonparametric conditions.

Suggested Citation

  • Heikki Kauppi, 2016. "The Generalized Receiver Operating Characteristic Curve," Discussion Papers 114, Aboa Centre for Economics.
    • Handle: RePEc:tkk:dpaper:dp114
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    References listed on IDEAS

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    5. Neumeyer, Natalie, 2004. "A central limit theorem for two-sample U-processes," Statistics & Probability Letters, Elsevier, vol. 67(1), pages 73-85, March.
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    Cited by:

    1. Sonia Pérez-Fernández & Pablo Martínez-Camblor & Peter Filzmoser & Norberto Corral, 2021. "Visualizing the decision rules behind the ROC curves: understanding the classification process," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 135-161, March.

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