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Better Bootstrap Confidence Intervals

Bradley Efron
Journal of the American Statistical Association
Vol. 82, No. 397 (Mar., 1987), pp. 171-185
DOI: 10.2307/2289144
Stable URL: http://www.jstor.org/stable/2289144
Page Count: 15
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Better Bootstrap Confidence Intervals
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Abstract

We consider the problem of setting approximate confidence intervals for a single parameter θ in a multiparameter family. The standard approximate intervals based on maximum likelihood theory, θ̂ ± σ̂z(α), can be quite misleading. In practice, tricks based on transformations, bias corrections, and so forth, are often used to improve their accuracy. The bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application, at the price of a considerable increase in computational effort. The new intervals incorporate an improvement over previously suggested methods, which results in second-order correctness in a wide variety of problems. In addition to parametric families, bootstrap intervals are also developed for nonparametric situations.

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