稳健主成分回归及其医学应用

摘要

Objective To explore the robust estimate method of principal component regression model. Methods Introduce a robust PCR which combines ROBPCA( robust principal component analysis) and robust regression- LTS ( least trimmed squares) method to establish model using a practical example. Results The robust principal component regression model has a better fitness than that of the original data in which outliers are not detected and removed. It is better to solve the outliers problem in PCR. Conclusion The robust principal component regression has a high robustness when there are outliers in PCR and should be widely used.%目的 探讨主成分回归模型的一种稳健估计方法.方法 将稳健主成分分析方法ROBPCA(robust principal component regression)和重新加权的LTS（least trimmed squares）方法结合起来,同时结合实例分析,建立稳健主成分回归方程,并可以生成诊断图来诊断异常点.结果 用含有异常点的原始数据得到的稳健模型,拟合效果较好.解决了主成分回归中存在异常点的问题.结论 当主成分回归中存在异常点时,本文中所述的稳健主成分回归方法具有较高的稳健性,有较好的应用前景.