Generalized likelihood ratio test for normal mixtures

@article{Jiang2016GeneralizedLR,
  title={Generalized likelihood ratio test for normal mixtures},
  author={Wenhua Jiang and Cun-Hui Zhang},
  journal={Statistica Sinica},
  year={2016}
}
Let X1, . . . , Xn be independent observations with Xi ∼ N(θi, 1), where (θ1, . . . , θn) is an unknown vector of normal means. Let fn(x) = ∑n i=1(d/dx)Pn{Xi ≤ x}/n be the average marginal density of observations. We consider the problem of testing H0 : fn ∈ F0, where F0 is a family of mixture densities. This includes detecting nonzero normal means with F0 = {fδ0} and testing homogeneity in mixture models with F0 = {fδμ}. We study a generalized likelihood ratio test (GLRT) based on the… 

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