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  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.