Nonparametric Estimation of the Precision-Recall Curve

The Precision-Recall (PR) curve is a widely used visual tool to evaluate the performance of scoring functions in regards to their capacities to discriminate between two populations. The purpose of this paper is to examine both theoretical and practical issues related to the statistical estimation of PR curves based on classification data. Consistency and asymptotic normality of the empirical counterpart of the PR curve in sup norm are rigorously established. Eventually, the issue of building confidence bands in the PR space is considered and a specific resampling procedure based on a smoothed and truncated version of the empirical distribution of the data is promoted. Arguments of theoretical and computational nature are presented to explain why such a bootstrap is preferable to a "naive" bootstrap in this setup.