Statistica Sinica 24 (2014), 773-797
Abstract: Randomization is described by Fisher (1935) as the reasoned basis for inference about the effectiveness of treatments. Fisher advocated both using randomization in designing experiments and using “randomization inference” to analyze experiments that have been randomized. Randomization inference is inference that assumes only the physical act of randomization for its validity. It provides exact, distribution free inferences in randomized experiments. In this paper, we expand the scope of randomization inference by developing randomization inference for the trimmed mean of effects attributable to treatment. Trimmed means of the effects attributable to treatment are interpretable summaries of the treatment effect that are robust to outliers. We connect the inference problem for trimmed means of effects attributable to treatment to a multiple choice knapsack problem, and use an efficient combinatorial optimization algorithm.
Key words and phrases: Knapsack problem, observational study, randomization inference, trimmed mean.