Semi-parametric estimation of treatment effects in randomised experiments

We develop new semi-parametric methods for estimating treatment effects. We focus on settings where the outcome distributions may be thick tailed, where treatment effects may be small, where sample sizes are large, and where assignment is completely random. This setting is of particular interest in recent online experimentation. We propose using parametric models for the treatment effects, leading to semi-parametric models for the outcome distributions. We derive the semi-parametric efficiency bound for the treatment effects for this setting, and propose efficient estimators. In the leading case with constant quantile treatment effects, one of the proposed efficient estimators has an interesting interpretation as a weighted average of quantile treatment effects, with the weights proportional to minus the second derivative of the log of the density of the potential outcomes. Our analysis also suggests an extension of Huber's model and trimmed mean to include asymmetry.

Automated summary

We propose new semi-parametric methods for estimating treatment effects in settings such as thick-tailed outcome distributions, small treatment effects, large sample sizes, and completely random assignment, which is of interest in online experimentation. Our approach uses parametric models for treatment effects and derives semi-parametric efficiency bound and efficient estimators. In the case of constant quantile treatment effects, one of our proposed estimators can be interpreted as a weighted average of quantile treatment effects, with weights proportional to the second derivative of the log density of potential outcomes. Our analysis also suggests extending Huber's model and trimmed mean to include asymmetry.