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\footnotesize \noindent Statistica Sinica {\bf 22} (2012), 1427-1456

\footnotesize \noindent doi:http://dx.doi.org/10.5705/ss.2010.167

\vspace{3pc} \normalsize \centerline{\large\bf A DIRECT
SEMIPARAMETRIC RECEIVER OPERATING} \vspace{2pt}
\centerline{\large\bf  CHARACTERISTIC CURVE REGRESSION WITH}
\vspace{2pt} \centerline{\large\bf  UNKNOWN LINK AND BASELINE
FUNCTIONS} \vspace{.25cm}
\author{Huazhen Lin$^1$, Xiao-Hua Zhou$^{2,3,4}$ and  Gang Li$^5$}
\vspace{.4cm} \centerline{\it $^1$Southwestern University of Finance
and Economics,} \centerline{\it  $^2$HSR$\&$D Center of Excellence,
$^3$University of Washington,} \centerline{\it $^4$Peking University
and $^5$University of California at Los Angeles} \vspace{.55cm}
\begin{quotation}
\noindent {\it Abstract:} In this article, we study a direct
receiver operating characteristic (ROC) curve regression model with
completely unknown link and baseline functions. A semiparametric
procedure is proposed to estimate both the parametric and
nonparametric components of the model. The resulting parameter
estimates and ROC curve estimates are shown to be consistent and
asymptotically normal with a $n^{-1/2}$ convergence rate. With
arbitrary link and baseline functions, our model is more robust than
existing direct ROC regression models that require either complete
or partially complete specification of the link and baseline
functions. Moreover, the robustness of our new method is gained at
little cost to efficiency, as evidenced
 by the parametric convergence rate
of our estimators and by the simulation study. An illustrative
example is given using a hearing test data set.\par \vspace{9pt}
\noindent {\it Key words and phrases:} Diagnostic tests, kernel
smoothing, nonparametric, ROC regression, transformation models.
\par
\end{quotation}
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