On Finite Gaussian Mixtures: Finiteness of the Number of Modes and an Application to NPMLE
We prove that every isotropic Gaussian mixture with finitely many components has finitely many modes. In one dimension, classical theory of Chebyshev systems gives the sharp bound of at most $n$ modes for an $n$-component mixture. In several dimensions, however, it has remained open whether every such mixture has finit...