The value of imperfect sample separation information in mixtures of normal distributions

This paper conducts a Monte Carlo study in order to evaluate the value of information in a normal mixture model when an imperfect sample separation indicator is available. For a variety of cases, computations are done on the ratios of asymptotic variances of the parameter estimators when sample separation is known versus when only the indicator is available. This study is patterned closely on a paper by Schmidt (1981), and obtains similar results when parameters appearing in Schmidt's model are allowed to vary. The new results here focus on the importance of the probabilities that the regime indicator is correct, for each of the two possible regimes.