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Variance Stabilization and the Bootstrap

Robert Tibshirani
Biometrika
Vol. 75, No. 3 (Sep., 1988), pp. 433-444
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2336593
Stable URL: http://www.jstor.org/stable/2336593
Page Count: 12
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Variance Stabilization and the Bootstrap
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Abstract

We investigate the use of a variance stabilizing transformation for the computation of a bootstrap t confidence interval. The transformation is estimated in an `automatic' manner through an initial bootstrap step. A bootstrap t interval is then computed for the variance stabilized parameter and the interval is mapped back to the original scale. The resultant procedure is second-order correct in some settings, invariant and in a number of examples it performs better than the usual untransformed bootstrap t interval. It also requires far less computation. The new interval is compared with Efron's BCa procedure and the two methods are seen to produce similar results.

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