Nonparametric test for density modes

A nonparametric resampling procedure is proposed to test the significance of a mode, with the aim of evaluating whether a region of relatively high observed density reflects the actual presence of a mode in the true distribution underlying a set of data. The method leverages on Morse theory and stochastic gradient methods to characterize the local properties of the modes. This allows the definition of an asymptotic test, based on the concept of gradient ascent paths and relying on resampling methods, to approximate the distribution of the test statistic under the null hypothesis.