Method of Moments Confidence Intervals for a Semi-Supervised Two-Component Mixture Model

TL;DR

This paper develops a method of moments approach to construct approximate confidence intervals for treatment effects in a semi-supervised two-component mixture model, without relying on parametric assumptions.

Contribution

It introduces a novel application of method of moments estimators for confidence intervals in mixture models with treatment effects.

Findings

Method of moments estimators effectively estimate treatment effects.

Confidence intervals can be obtained without parametric assumptions.

The approach is useful for semi-supervised mixture models.

Abstract

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 paper, we investigate properties of the method of moment estimators for the treatment effect and demonstrate their usefulness for obtaining approximate confidence intervals without any parametric assumptions about the distribution of responses.