Third Year Candidacy Requirement: "Bootstrap for Extremes"

Abstract: Efron's Bootstrap is known to be inefficient in certain scenarios, one of them being the extremes of independent and identically distributed random variables when the resample- and the sample sizes are equal.

In such cases, the m out of n Bootstrap is used, with m = o(n). The consistency of the m out of n Bootstrap with m= o(n) has been widely investigated. However, the choice of m is critical in ensuring the optimal performance of the method. In this presentation, we will do a brief literature review of univariate extreme value theory, and m out of n Bootstrap, and mention our findings on the optimal choice of m in the m out of n Bootstrap.

Host: Soumendra Lahiri