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Abstract:
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ROC curve is defined as true positive rate versus false positive rate obtained by varying a decision threshold criterion. Mathematically speaking, ROC curve is a composition of survival function of one population to the quantile function of another population. In this paper, we study strong approximation for the quantile processes of bootstrap and the Bayesian bootstrap resampling distributions, and use this result to study strong approximations for the empirical ROC estimator, the corresponding bootstrap, and the Bayesian versions in terms of two independent Kiefer processes. The results imply asymptotically accurate coverage probabilities for bootstrap and the Bayesian bootstrap confidence bands, and accurate frequentist coverage probabilities of bootstrap and the Bayesian bootstrap confidence intervals for the area under the curve functional of the ROC.
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