Penalized spline models for functional principal component analysis
Penalized spline models for functional principal component analysis
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DOI：
10.1111/j.1467-9868.2005.00530.x
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发表时间：
2006-02
期刊：
影响因子：
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通讯作者：
Fang Yao;Thomas C. M. Lee
中科院分区：
文献类型：
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作者：
Fang Yao;Thomas C. M. Lee
摘要我们提出了一个迭代估计过程进行功能主成分分析。该程序的目的是功能或纵向数据，其中来自同一受试者的重复测量是相关的。一个越来越流行的平滑方法，惩罚样条回归，被用来表示的平均函数。这允许直接纳入协变量和简单的实施近似推理程序的系数。为了处理受试者内相关性，我们开发了一种迭代程序，该程序减少了对同一受试者进行的重复测量之间的依赖性。迭代后得到的数据在理论上被证明是渐近等价（概率）的一组独立的数据。这表明，惩罚样条回归的一般理论，已开发的独立数据也可以应用于功能数据。所提出的方法的有效性证明通过模拟研究和应用酵母细胞周期基因表达数据。
Summary. We propose an iterative estimation procedure for performing functional principal component analysis. The procedure aims at functional or longitudinal data where the repeated measurements from the same subject are correlated. An increasingly popular smoothing approach, penalized spline regression, is used to represent the mean function. This allows straightforward incorporation of covariates and simple implementation of approximate inference procedures for coefficients. For the handling of the within‐subject correlation, we develop an iterative procedure which reduces the dependence between the repeated measurements that are made for the same subject. The resulting data after iteration are theoretically shown to be asymptotically equivalent (in probability) to a set of independent data. This suggests that the general theory of penalized spline regression that has been developed for independent data can also be applied to functional data. The effectiveness of the proposed procedure is demonstrated via a simulation study and an application to yeast cell cycle gene expression data.