Non-parametric smoothed estimation of multivariate cumulative distribution and survival functions, and receiver operating characteristic curves

Abstract

A unified framework to analyse multivariate kernel estimators of distribution and survival functions is introduced, before turning our attention to receiver operating characteristic (ROC) curves. These are well-established visual analytic tools for univariate data samples, though their generalisation to multivariate data has been limited. Since non-parametric multivariate kernel smoothing methods possess excellent visualisation properties, they serve as a solid basis for their estimation. With optimal data-based bandwidth matrix selectors, we demonstrate that they possess suitable properties for exploratory data analysis of simulated and experimental data.