Breakdown theory for bootstrap quantiles

A general formula for computing the breakdown point (in robustness) for the tth bootstrap quantile of a statistic T-n is obtained. The answer depends on t and the breakdown point of T-n. Since the bootstrap quantiles are vital ingredients of bootstrap confidence intervals, the theory has implications pertaining to robustness of bootstrap confidence intervals. For certain L and M estimators, a robustification of bootstrap is suggested via the notion of Winsorization.