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摘要翻译：
本文研究了从稀疏不规则纵向观测数据中估计协方差核（即泛函主成分）的特征值和特征函数的问题。假设协方差核是光滑的、有限维的，我们通过极大似然方法来处理这个问题。我们利用特征函数的光滑性，通过将特征函数限制在光滑函数的低维空间来降低维数。该估计格式基于Newton-Raphson过程，利用代表本征函数的基系数位于Stiefel流形上这一事实来发展。我们还讨论了正确的基函数数目的选择，以及协方差核的维数的选择，这是通过一个二阶近似的左一曲线外交叉验证得分，这是非常有效的计算。通过仿真研究和对CD4计数数据集的应用，证明了该方法的有效性。在仿真研究中，我们的方法在估计和模型选择方面都取得了很好的效果。它也优于现有的两种方法：一种是基于经验协方差的局部多项式平滑，另一种是使用EM算法。
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英文标题：
《A geometric approach to maximum likelihood estimation of the functional
principal components from sparse longitudinal data》
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作者：
Jie Peng and Debashis Paul
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最新提交年份：
2007
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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英文摘要：
In this paper, we consider the problem of estimating the eigenvalues and eigenfunctions of the covariance kernel (i.e., the functional principal components) from sparse and irregularly observed longitudinal data. We approach this problem through a maximum likelihood method assuming that the covariance kernel is smooth and finite dimensional. We exploit the smoothness of the eigenfunctions to reduce dimensionality by restricting them to a lower dimensional space of smooth functions. The estimation scheme is developed based on a Newton-Raphson procedure using the fact that the basis coefficients representing the eigenfunctions lie on a Stiefel manifold. We also address the selection of the right number of basis functions, as well as that of the dimension of the covariance kernel by a second order approximation to the leave-one-curve-out cross-validation score that is computationally very efficient. The effectiveness of our procedure is demonstrated by simulation studies and an application to a CD4 counts data set. In the simulation studies, our method performs well on both estimation and model selection. It also outperforms two existing approaches: one based on a local polynomial smoothing of the empirical covariances, and another using an EM algorithm.
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PDF链接：
https://arxiv.org/pdf/710.5343
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