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Biometrika 1999 86(3):487-502; doi:10.1093/biomet/86.3.487
© 1999 by Biometrika Trust
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Semiparametric inference for a quantile comparison function with applications to receiver operating characteristic curves

G LiA, RC TiwariA2 and MT WellsA3

A Department of Biostatistics, School of Public Health, University of California, Los Angeles, CA 90095, USA E-mail: gangli@sunlab.ph.ucla.edu A2 Department of Mathematics, University of North Carolina, Charlotte, NC 28223, USA A3 Department of Social Statistics, Cornell University, Ithaca, NY 14853, USA E-mail: mtw1@cornell.edu

In studies to compare two samples, more information may be available on one treatment than the other. When one population is modelled parametrically and the other nonparmetrically, we study large sample properties of a semiparametric sample quantile comparison function and show that it can have substantially smaller asymptotic variance than its nonparametric counterpart, especially near the boundaries. We describe applications to both two-sample tests and receiver operating characteristic curves.

Key Words: Bootstrap; Censored data; Khmaladze transform; Kolmogorov-type test; Martingale; Percentile-percentile plot; Sensitivity; Specificity; Two-sample problem


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