Nonparametric and semiparametric estimation of the receiver operating characteristic curve

Minimum distance estimation of the binormal ROC curve

“…We obtain that the MDE given by Hsieh and Turnbull (1996) outperforms, in some sense, MDE given by Davidov and Nov (2012). Both of the estimators are obtained by minimization of distance measures between the unknown binormal and empirical ROC curve.…”

“…In this paper we compare the accuracy of the known MDE's given by Hsieh and Turnbull (1996) and Davidov and Nov (2012). We obtain that the MDE given by Hsieh and Turnbull (1996) outperforms, in some sense, MDE given by Davidov and Nov (2012).…”

“…Metz et al (1998) developed an algorithm called LABROC, which groups continuous data into a finite number of ordered categories and then uses the maximum likelihood algorithm from Dorfman and Alf (1969). Hsieh and Turnbull (1996) proposed a generalized least squares procedure for grouped data and a minimum distance estimator (MDE), which does not require grouping data. MDE of the binormal ROC curve was also considered in the papers of Nov (2009, 2012).…”

“…To the best of our knowledge, a minimum distance approach to estimating the binormal ROC curve parameters was considered only by Hsieh and Turnbull (1996) and Nov (2009, 2012). In the paper of Davidov and Nov (2009) the central idea was to estimate the unknown function h (a transformation of X and Y to normal random variables) in two different ways; only one of the two estimates depended on the unknown parameters μ and σ of the binormal ROC curve.…”

“…Then, they estimated μ and σ by the values that minimized a certain norm of the difference between the estimates of the function h. In this paper we do not develop this idea. A different approach is presented in the papers of Hsieh and Turnbull (1996) and Davidov and Nov (2012). They took into consideration two different measures of distance between the empirical and the theoretical ordinal dominance curve (ODC), the curve closely related to the ROC curve.…”