Multivariate Modality Inference Using Gaussian Kernel

Abstract

The number of modes (also known as modality) of a kernel density estimator (KDE) draws lots of interests and is important in practice. In this paper, we develop an inference framework on the modality of a KDE under multivariate setting using Gaussian kernel. We applied the modal clustering method proposed by [1] for mode hunting. A test statistic and its asymptotic distribution are derived to assess the significance of each mode. The inference procedure is applied on both simulated and real data sets.