Statistica Sinica 10(2000), 1-50
HYBRID RESAMPLING METHODS FOR CONFIDENCE
INTERVALS
Chin-Shan Chuang and Tze Leung Lai
Carnegie-Mellon University and Stanford University
Abstract:
This paper considers the problem of constructing confidence intervals
for a single parameter 
in a multiparameter or nonparametric
family. Hybrid resampling methods, which ``hybridize'' the essential
features of bootstrap and exact methods, are proposed and developed
for both parametric and nonparametric situations. In particular,
we apply such methods to construct confidence regions, whose
coverage probabilities are nearly equal to the nominal ones, for
the treatment effects associated with the primary and secondary
endpoints of a clinical trial whose stopping rule, specified by
a group sequential test, makes the approximate pivots in the
nonsequential bootstrap method highly ``non-pivotal''. We also
apply hybrid resampling methods to construct second-order correct
confidence intervals in possibly non-ergodic autoregressive models
and branching processes.
Key
words and phrases:
Bootstrap confidence intervals,
empirical likelihood, group sequential tests, hybrid resampling,
nonparametric tilting.