Robust Bootstrap

Our robust bootstrap deals with the two problems mentioned above. On the one hand, each evaluation of our bootstrapped estimator is just a linear combination of the re-sampled points so that the computing requirement is minimal. On the other hand, we sample the data paired with weights so that outlying observations are down-weighted. The resulting estimate will not breakdown as long as the bootstrap sample contains at least one ``good'' point. For simplicity, I will first present our robust bootstrap in the location model with known scale. The more general location-scale setup is presented immediately after.