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Statistica Sinica 10(2000), 1-50



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 $\theta$ 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.

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