Rudy Beran, UC Davis

"On double bootstrap asymptotics"

Peter Hall and I first met through discovery of our mutual interest in the iterated bootstrap (Beran 1987, Hall and Martin 1988). In particular, the iterated bootstrap provides a unifying Algorithmic User Interface to finding more accurate critical values for confidence sets, whether this is done by algebraic or Monte Carlo techniques. My talk describes several examples of effective iterated bootstrap confidence sets: Welch's solution to the Behrens-Fisher problem and beyond; improving upon the Bartlett adjustment to likelihood ratio confidence sets; refining the family-wise coverage probability and balance of simultaneous confidence sets; and sharpening the coverage probability of Stein confidence sets.