In the causal inference literature a class of semi-parametric estimators is called robust if the estimator has desirable properties under the assumption that at least one of the working models is correctly specified. A standard example is a doubly robust estimator that specifies parametric...

An estimand of interest in empirical studies with observational data is the average treatment effect of a multi-valued treatment in the treated subpopulation. We demonstrate three estimation approaches: outcome regression, inverse probability weighting and inverse probability weighted...