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Kauppi, Heikki
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Series/Report no.: 
Discussion paper No. 114
Aboa Centre for Economics (ACE), Turku
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=1) and alpha =Pr (D=1=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.
classification problem
receiver operating characteristic (ROC) curve
likelihood ratio rule
semi-parametric estimation
non-parametric estimation
Document Type: 
Working Paper

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