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Prepivoting to Reduce Level Error of Confidence Sets

Rudolf Beran
Biometrika
Vol. 74, No. 3 (Sep., 1987), pp. 457-468
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2336685
Stable URL: http://www.jstor.org/stable/2336685
Page Count: 12
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Prepivoting to Reduce Level Error of Confidence Sets
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Abstract

Approximate confidence sets for a parameter θ may be obtained by referring a function of θ and of the sample to an estimated quantile of that function's sampling distribution. We call this function the root of the confidence set. Either asymptotic theory of bootstrap methods can be used to estimate the desired quantile. When the root is not a pivot, in the sense of classical statistics, the actual level of the approximate confidence set may differ substantially from the intended level. Prepivoting is the transformation of a confidence set root by its estimated bootstrap cumulative distribution function. Prepivoting can be iterated. Bootstrap confidence sets generated from a root prepivoted one or more times have smaller error in level than do confidence sets based on the original root. The first prepivoting is nearly equivalent to studentizing, when that operation is appropriate. Further iterations of prepivoting make higher order corrections automatically.

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