BOOTSTRAP CONFIDENCE-INTERVALS FOR A CLASS OF PARAMETRIC PROBLEMS
BOOTSTRAP CONFIDENCE-INTERVALS FOR A CLASS OF PARAMETRIC PROBLEMS
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DOI：
10.1093/biomet/72.1.45
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发表时间：
1985-01-01
期刊：
影响因子：
2.7
通讯作者：
EFRON, B
中科院分区：
文献类型：
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作者：
EFRON, B
我们考虑如下一类问题：在观察了一个均值向量为η，协方差矩阵为单位的多元正态数据向量后，找到了η的实值函数？=t(L1)的一个近似的可信区间。给出了一种简单的几何结构，可以得到高精度的解。这种构造表明，当？在σ中是非线性的时，基于极大似然理论的标准近似？？7plusMn；αz(η)可能具有很大的误导性。我们讨论了基于Bootstrap的置信度区间，它以相当多的计算为代价消除了标准近似中的大部分误差。在η和Bootstrap的变换下，Bootstrap区间是不变的，因此在可以转换为多元正态的问题中，它们自动产生准确的解，而不需要知道归一化变换。
We consider the following class of problems: having observed a multivariate normal data vectorywith unknown mean vector η, covariance matrix the identity, find an approximate confidence interval for ø = t(η), a real-valued function of η. A simple geometric construction is given which leads to highly accurate solutions. This construction shows that the standard approximation based on maximum likelihood theory, ø7plusmn;σz(α), can be quite misleading when ø is nonlinear in η. We discuss bootstrap-based confidence intervals which remove most of the error in the standard approximation, at the expense of considerably more calculation. The bootstrap intervals are invariant under transformation of bothyand η, and so they automatically produce accurate solutions in problems which can be transformed to multivariate normality, without requiring knowledge of the normalizing transformation.