Risk bounds for mixture density estimation

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Variational Boosting: Iteratively Refining Posterior Approximations (2016, unknown): “Sequential maximum-likelihood estimation of mixture models has been studied previously where the error between the sequentially learned model and the optimal model where all components and weights are jointly learned is bounded by O(1/C) where C is the number of mixture components (Li & Barron, 1999”
Likelihood Ratio-Based Biometric Score Fusion (2008, methodology): “Gaussian mixture model (GMM) has been successfully used to estimate arbitrary densities and the theoretical results in [14], [15] show that the density estimates obtained using finite mixture models indeed converge to the true density when a sufficient number of training samples are available.”