Testing homogeneity in a heteroscedastic contaminated normal mixture

Testing homogeneity in contaminated mixture models

“…where p(𝜆) is a penalty function of 𝜆 which prevents the fit of 𝜆 being close to 0. Following Fu, Chen & Li (2008) and Niu, Li & Fu (2019), we choose p(𝜆) = log(𝜆). The selection of penalty function p n (𝛾 2 ) for each component case is discussed in Section 3.…”

“…Dai & Charnigo (2008, 2010 employed contaminated Beta mixtures and contaminated normal mixtures for a pilot study in large-scale multiple testing problems, for example, in gene filtration studies. Fan (2014) and Niu, Li & Fu (2019) focused on contaminated normal models and analyzed a Down syndrome microarray dataset and a dataset about pedestrian stops by police, respectively.…”

“…By filtering out batches of genes, the efficiency and accuracy of large-scale multiple testing can be significantly improved. Recently, Niu, Li & Fu (2019) relaxed the homoscedasticity assumption in Dai & Charnigo (2010) and proposed an EM-test to test homogeneity in a heteroscedastic, contaminated normal mixture model. Their simulation studies and real-data analysis showed that the EM-test has better performance in terms of type I error and power than the tests in Dai & Charnigo (2008, 2010.…”

“…To the best of our knowledge, for testing Equation (2) under the CMM given by model (1) (the case with no extra assumption on 𝛾 1 = 𝛾 2 ), only the heteroscedastic contaminated normal mixture has been studied in the literature. Motivated by the EM-test proposed by and Li, Chen & Marriott (2009), Niu, Li & Fu (2019) recently established a new EM-test to test Equation ( 2) with a special focus on a normal kernel. They adopted a penalized likelihood approach to deal with the unboundedness of the likelihood function.…”

“…The proposed test and its asymptotic results are applicable to many CMMs whose kernel distributions are normal, logistic, type I extreme value, generalized Student's t, gamma or von Mises. Note that to deal with the unboundedness of the likelihood function, we take a slightly different approach from that of Niu, Li & Fu (2019). More specifically, we found that we only need to add a penalty function on the parameter 𝛾 2 , while a penalty on 𝛾 1 is, in fact, unnecessary.…”