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\subsection{Excess-mass method (EMM)} \label{sec:methods-emm}  As described in Secetion (\ref{sec:methods-gmm}), GMM-based statistics can make relable inference on varies aspects, such as likelihood, bandwidth and kurtosis test. But it should be emphsised here that all of them have a fundamental assumption on the Gaussianality of all modes. Sometimes, however, this prior information cannot be obtained beforehand. It is then important to have an alternative test statisitics, which does not require the explicit functional form of the distribution for modes. Here we introduce a pure geometric method, excess mass estimates, to measure excessive empirical mass with multi-modes v.s. uni-mode developed by \citet{muller_sawitzki91}.  \subsection{Bootstrap}