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Variance stabilization and the bootstrap. (English) Zbl 0651.62039
Summary: 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 {\it B. Efron}’s $BC\sb a$ procedure [J. Am. Stat. Assoc. 82, 171-200 (1987; Zbl 0622.62039)] and the two methods are seen to produce similar results.

MSC:
62G15Nonparametric tolerance and confidence regions
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