Fitting a Finite Mixture Distribution to a Variable Subject to Heteroscedastic Measurement Error

We consider the case where a latent variable X cannot be observed
directly and instead a variable W=X+U with an heteroscedastic
measurement error U is observed. It is assumed that the
distribution of the true variable X is a mixture of normals and a
type of the EM algorithm is applied to find approximate ML
estimates of the distribution parameters of X.