  We develop new semiparametric 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 semiparametric models for the outcome
distributions. We derive the semiparametric 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.
