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ON STUDENTIZING AND BLOCKING METHODS FOR IMPLEMENTING THE BOOTSTRAP WITH DEPENDENT DATA
Author(s) -
Davison A.C.,
Hall Peter
Publication year - 1993
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1993.tb01327.x
Subject(s) - studentized range , percentile , estimator , blocking (statistics) , statistic , computer science , mathematics , variance (accounting) , bootstrapping (finance) , statistics , econometrics , standard deviation , business , accounting
Summary Gōtze & Kūnsch (1990) announced that a certain version of the bootstrap percentile‐ t method, and the blocking method, can be used to improve on the normal approximation to the distribution of a Studentized statistic computed from dependent data. This paper shows that this result depends fundamentally on the method of Studentization. Indeed, if the percentile‐ t method is implemented naively, for dependent data, then it does not improve by an order of magnitude on the much simpler normal approximation despite all the computational effort that is required to implement it. On the other hand, if the variance estimator used for the percentile‐ t bootstrap is adjusted appropriately, then percentile‐ t can improve substantially on the normal approximation.