Open Access
February 1996 Nonparametric and semiparametric estimation of the receiver operating characteristic curve
Fushing Hsieh, Bruce W. Turnbull
Ann. Statist. 24(1): 25-40 (February 1996). DOI: 10.1214/aos/1033066197


The receiver operating characteristic (ROC) curve describes the performance of a diagnostic test used to discriminate between healthy and diseased individuals based on a variable measured on a continuous scale. The data consist of a training set of m responses $X_1, \dots, X_m$ from healthy individuals and n responses $Y_1, \dots, Y_n$ from diseased individuals. The responses are assumed i.i.d. from unknown distributions F and G, respectively. We consider estimation of the ROC curve defined by $1 - G(F^{-1} (1 - t))$ for $0 \leq t \leq 1$ or, equivalently, the ordinal dominance curve (ODC) given by $F(G^{-1} (t))$. First we consider nonparametric estimators based on empirical distribution functions and derive asymptotic properties. Next we consider the so-called semiparametric "binormal" model, in which it is assumed that the distributions F and G are normal after some unknown monotonic transformation of the measurement scale. For this model, we propose a generalized least squares procedure and compare it with the estimation algorithm of Dorfman and Alf, which is based on grouped data. Asymptotic results are obtained; small sample properties are examined via a simulation study. Finally, we describe a minimum distance estimator for the ROC curve, which does not require grouping the data.


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Fushing Hsieh. Bruce W. Turnbull. "Nonparametric and semiparametric estimation of the receiver operating characteristic curve." Ann. Statist. 24 (1) 25 - 40, February 1996.


Published: February 1996
First available in Project Euclid: 26 September 2002

zbMATH: 0855.62029
MathSciNet: MR1389878
Digital Object Identifier: 10.1214/aos/1033066197

Primary: 62G07
Secondary: 62G20 , 62H30

Keywords: Binormal model , ‎classification‎ , diagnostic test , discrimination , nonparametric estimation , receiver operating characteristic (ROC) , semiparametric models

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 1 • February 1996
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