ESTIMATION OF THE VARIANCE FOR THE MAXIMUM LIKELIHOOD ESTIMATES IN NORMAL MIXTURE MODELS AND NORMAL HIDDEN MARKOV MODELS

Abstract

In this article, we derive the observed information matrices for normal mixture models and normal hidden Markov models. We also describe the parametric bootstrap method for the said models. The matrices and the method mentioned above are used to estimate the variance of the maximum likelihood estimates (MLEs) obtained by the Expectation-Maximization (EM) algorithm. Finally, a numerical example is shown using a data set named \faithful" given in the free statistical software R.