Parameter estimation with profile likelihood method and penalized EM algorithm in normal mixture distributions

As we know, as the likelihood function of the normal mixture is not a bounded function on 𝚯, a global maximum likelihood estimation(MLE) can not always be found and use of an EM (Expectation-Maximization) algorithm can possible lead towards a degenerate solution.In this study, the purpose was to determine which method has a better estimate to parameters of univariate two-component normal mixture distribution, as comparing profile likelihood method and penalized EM in unequal variance and to avoid from unbounded of log-likelihood function and to maximization to likelihood function.For this purpose a simulation study was performed. Thus, we tried to determine which algorithm gives a better estimate for the parameters.