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A mixture of a distribution of responses from untreated patients and a shift of that distribution is a useful model for the responses from a group of treated patients. The mixture model accounts for the fact that not all the patients in the treated group will respond to the treatment and consequently their responses follow the same distribution as the responses from untreated patients. The treatment effect in this context consists of both the fraction of the treated patients that are responders and the magnitude of the shift in the distribution for the responders. In this article, we investigate asymptotic properties of method of moment estimators for the treatment effect based on a semi-supervised two-component mixture model. From these properties, we develop asymptotic confidence intervals and demonstrate their superior statistical inference performance compared to the computationally intensive bootstrap intervals and their Bias-Corrected versions.

Statistical Inference for Method of Moments Estimators of a Semi-Supervised Two-Component Mixture Model