JinSeo.Cho - Practical Testing for Normal Mixtures

<Abstract> The current study provides the Gaussian versions used to test for normal mixtures. These versions are highly practical as they can directly be used to simulate the asymptotic critical values of standard tests, for example the likelihood-ratio or Lagrange multiplier tests. We investigate testing for two normal mixtures: one having a single variance and two distinct means, and another having a single mean and two different variances. We derive the Gaussian versions for the two models by associating the score functions with the Hermite and generalized Laguerre polynomials, respectively. Additionally, we compare the performance of the likelihood-ratio and Lagrange multiplier tests using the asymptotic critical values.