Confidence intervals (CIs) in principal component analysis (PCA) can be based on asymptotic standard errors and on the bootstrap methodology. The present paper offers an overview of possible strategies for bootstrapping in PCA. A motivating example shows that CI estimates for the component loadings using different methods may diverge. We explain that this results from both differences in quality and in perspective on the rotational freedom of the population loadings. A comparative simulation study examines the quality of various estimated component loading CIs. The bootstrap approach is more flexible and generally yields better CIs than the asymptotic approach. However, in the case of a clear simple structure of varimax rotated loadings, one can be confident that the asymptotic estimates are reasonable as well.

中文翻译：

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估计主成分载荷的置信区间：自举和渐近结果之间的比较。

主成分分析（PCA）中的置信区间（CI）可以基于渐近标准误差和自举方法。本文概述了PCA中自举的可能策略。一个令人鼓舞的例子表明，使用不同方法对组件负载的CI估计可能会有所不同。我们解释说，这是由于质量差异和人口负载旋转自由度方面的差异造成的。一项比较仿真研究检查了各种估计的组件加载CI的质量。自举方法比渐进方法更灵活，通常可产生更好的CI。但是，在varimax旋转载荷的清晰简单结构的情况下，人们可以确信渐近估计也是合理的。