Breakdown point theory for implied probability bootstrap

Summary  This paper studies robustness of bootstrap inference methods under moment conditions. In particular, we compare the uniform weight and implied probability bootstraps by analysing behaviours of the bootstrap quantiles when outliers take arbitrarily large values, and derive the breakdown points for those bootstrap quantiles. The breakdown point properties characterize the situation where the implied probability bootstrap is more robust against outliers than the uniform weight bootstrap. Simulation studies illustrate our theoretical findings.