A general formula for computing the breakdown point in robustness for the tth bootstrap quantile of a statistic Tₙ is obtained. The answer depends on t and the breakdown point of Tₙ. 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.
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Kesar Singh (1998) studied this question.
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