Bootstrap Confidence Intervals for a Class of Parametric Problems
针对多元正态数据中均值向量的实值函数，提出一种几何构造方法，发现标准近似可能误导，而自助法置信区间能消除大部分误差，且具有变换不变性。
We consider the following class of problems: having observed a multivariate normal data vector y with 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 both y and η, and so they automatically produce accurate solutions in problems which can be transformed to multivariate normality, without requiring knowledge of the normalizing transformation.