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Biometrika 1987 74(3):481-493; doi:10.1093/biomet/74.3.481
© 1987 by Biometrika Trust
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On the bootstrap and likelihood-based confidence regions

PETER HALL

Department of Statistics, Australian National University Canberra, ACT 2601, Australia

We describe a method for constructing likelihood-based confidence regions for a vector parameter, using the bootstrap and nonparametric density estimation. The technique is illustrated by application to a numerical example, and its theoretical properties are elucidated. It is argued that likelihood-based regions should not be approximated by ellipses, if we are to have any hope of capturing first-order departures from normality. Bootstrap algorithms for constructing simultaneous confidence intervals for the components of a vector parameter are also presented. Advantages of the percentile-t method over the ordinary percentile method are demonstrated in a multivariate setting.

Key Words: Bootstrap • Likelihood-based confidence region • Nonparametric density estimation • Percentile method • Percentile-t method • Simultaneous confidence intervals


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[Abstract]


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