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Multilevel sparse functional principal component analysis.
Stat ( IF 1.7 ) Pub Date : 2014-04-24 , DOI: 10.1002/sta4.50 Chongzhi Di 1 , Ciprian M Crainiceanu 2 , Wolfgang S Jank 3
Stat ( IF 1.7 ) Pub Date : 2014-04-24 , DOI: 10.1002/sta4.50 Chongzhi Di 1 , Ciprian M Crainiceanu 2 , Wolfgang S Jank 3
Affiliation
We consider analysis of sparsely sampled multilevel functional data, where the basic observational unit is a function and data have a natural hierarchy of basic units. An example is when functions are recorded at multiple visits for each subject. Multilevel functional principal component analysis was proposed recently for such data when functions are densely recorded. Here, we consider the case when functions are sparsely sampled and may contain only a few observations per function. We exploit the multilevel structure of covariance operators and achieve data reduction by principal component decompositions at both between‐subject and within‐subject levels. We address inherent methodological differences in the sparse sampling context to: (i) estimate the covariance operators; (ii) estimate the functional principal component scores; and (iii) predict the underlying curves. Through simulations, the proposed method is able to discover dominating modes of variations and reconstruct underlying curves well even in sparse settings. Our approach is illustrated by two applications, the Sleep Heart Health Study and eBay auctions. Copyright © 2014 John Wiley & Sons, Ltd
中文翻译:
多级稀疏函数主成分分析。
我们考虑分析稀疏采样的多级函数数据,其中基本观测单元是一个函数,数据具有基本单元的自然层次结构。一个例子是在每个主题的多次访问中记录功能。当函数被密集记录时,最近针对此类数据提出了多级函数主成分分析。在这里,我们考虑函数被稀疏采样并且每个函数可能只包含几个观察值的情况。我们利用协方差算子的多级结构,通过主体间和主体内的主成分分解实现数据缩减。我们解决了稀疏采样上下文中固有的方法论差异:(i)估计协方差算子;(ii) 估计功能主成分得分;(iii) 预测基础曲线。通过模拟,即使在稀疏设置中,所提出的方法也能够发现变化的主导模式并很好地重建底层曲线。我们的方法通过两个应用程序来说明:睡眠心脏健康研究和 eBay 拍卖。版权所有 © 2014 John Wiley & Sons, Ltd
更新日期:2014-04-24
中文翻译:
多级稀疏函数主成分分析。
我们考虑分析稀疏采样的多级函数数据,其中基本观测单元是一个函数,数据具有基本单元的自然层次结构。一个例子是在每个主题的多次访问中记录功能。当函数被密集记录时,最近针对此类数据提出了多级函数主成分分析。在这里,我们考虑函数被稀疏采样并且每个函数可能只包含几个观察值的情况。我们利用协方差算子的多级结构,通过主体间和主体内的主成分分解实现数据缩减。我们解决了稀疏采样上下文中固有的方法论差异:(i)估计协方差算子;(ii) 估计功能主成分得分;(iii) 预测基础曲线。通过模拟,即使在稀疏设置中,所提出的方法也能够发现变化的主导模式并很好地重建底层曲线。我们的方法通过两个应用程序来说明:睡眠心脏健康研究和 eBay 拍卖。版权所有 © 2014 John Wiley & Sons, Ltd