  We provide a comprehensive theory of conducting in-sample statistical
inference about receiver operating characteristic (ROC) curves that are based
on predicted values from a first stage model with estimated parameters (such as
a logit regression). The term "in-sample" refers to the practice of using the
same data for model estimation (training) and subsequent evaluation, i.e., the
construction of the ROC curve. We show that in this case the first stage
estimation error has a generally non-negligible impact on the asymptotic
distribution of the ROC curve and develop the appropriate pointwise and
functional limit theory. We propose methods for simulating the distribution of
the limit process and show how to use the results in practice in comparing ROC
curves.
