论文标题
稀疏纵向数据的强大功能主成分
Robust functional principal components for sparse longitudinal data
论文作者
论文摘要
在本文中，我们回顾了可靠的功能主成分分析（FPCA）的现有方法，并提出了一种新方法，可以应用于纵向数据，在纵向数据中，每个轨迹只有少数观察值可用。该方法与非典型观测值的存在是鲁棒的，也可以用于为稀疏观察到的功能数据得出一种新的非运动FPCA方法。我们使用局部回归来估计协方差函数的值，利用以下事实：对于椭圆形分布的随机向量，其某些组件的条件位置参数给出了其他组件的条件位置参数是条件集的线性函数。该观察结果使我们能够使用强大的局部回归方法获得强大的FPCA估计器。通过一项模拟研究探讨了我们提案的有限样本性能，该研究表明，正如预期的那样，当数据污染时，强大的方法优于现有替代方案。此外，我们还看到，对于不包含异常值的样本，我们的提案的不持胸表变体与文献中现有的替代方案相比有利。还提出了一个真实的数据示例。
In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This method is robust against the presence of atypical observations, and can also be used to derive a new non-robust FPCA approach for sparsely observed functional data. We use local regression to estimate the values of the covariance function, taking advantage of the fact that for elliptically distributed random vectors the conditional location parameter of some of its components given others is a linear function of the conditioning set. This observation allows us to obtain robust FPCA estimators by using robust local regression methods. The finite sample performance of our proposal is explored through a simulation study that shows that, as expected, the robust method outperforms existing alternatives when the data are contaminated. Furthermore, we also see that for samples that do not contain outliers the non-robust variant of our proposal compares favourably to the existing alternative in the literature. A real data example is also presented.
