It is of great interest to conduct robust functional principal component analysis (FPCA) that can identify the major modes of variation in the stochastic process with the presence of outliers. A new robust FPCA method is proposed in a new regression framework. An M-estimator for the functional principal components is developed based on the Huber’s loss by iteratively fitting the residuals from the Karhunen–Lovève expansion for the stochastic process under the robust regression framework. Our method can naturally accommodate sparse and irregularly-sampled data. When the functional data have outliers, our method is shown to render stable and robust estimates of the functional principal components; when the functional data have no outliers, we show via simulation studies that the performance of our approach is similar to that of the conventional FPCA method. The proposed robust FPCA method is demonstrated by analyzing the Hawaii ocean oxygen data and the kidney glomerular filtration rates for patients after renal transplantation.

进行稳健的功能主成分分析 (FPCA) 可以识别存在异常值的随机过程中的主要变化模式是非常有趣的。在新的回归框架中提出了一种新的鲁棒 FPCA 方法。功能主成分的 M 估计量是基于 Huber 的损失，通过在稳健回归框架下迭代拟合随机过程的 Karhunen-Lovève 展开的残差来开发的。我们的方法可以自然地适应稀疏和不规则采样的数据。当函数数据有异常值时，我们的方法被证明可以对函数主成分进行稳定和稳健的估计；当功能数据没有异常值时，我们通过模拟研究表明，我们的方法的性能类似于传统的 FPCA 方法。通过分析夏威夷海洋氧气数据和肾移植后患者的肾小球滤过率，证明了所提出的稳健 FPCA 方法。