Corrected confidence bands for functional data using principal components.
Corrected confidence bands for functional data using principal components.
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DOI：
10.1111/j.1541-0420.2012.01808.x
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发表时间：
2013-03
期刊：
影响因子：
1.9
通讯作者：
Crainiceanu C
中科院分区：
文献类型：
--
作者：
Goldsmith J;Greven S;Crainiceanu C
函数型主成分分析被广泛用于分解和表达函数型观测值。曲线估计隐含地取决于基函数和来自FPC分解的其他量;然而，这些对象在实践中是未知的。在这篇文章中，我们提出了一种方法，通过考虑FPC分解中的不确定性来获得正确的曲线估计。此外，逐点和同时置信区间，占模型和分解为基础的变异性。函数展开式的标准混合模型表示用于构造特定分解条件下的曲线估计值和方差。迭代期望和方差公式结合了联合收割机在分解分布中基于模型的条件估计值。一个引导程序来理解主成分分解量的不确定性。我们的方法相比，有利的竞争方法在模拟研究，包括密集和稀疏观察的功能。我们将我们的方法应用于稀疏的CD 4细胞计数和密集的白质束配置文件的观察。分析和模拟的代码是公开的，我们的方法是在CRAN的R包退款中实现的。
Functional principal components (FPC) analysis is widely used to decompose and express functional observations. Curve estimates implicitly condition on basis functions and other quantities derived from FPC decompositions; however these objects are unknown in practice. In this article, we propose a method for obtaining correct curve estimates by accounting for uncertainty in FPC decompositions. Additionally, pointwise and simultaneous confidence intervals that account for both model- and decomposition-based variability are constructed. Standard mixed model representations of functional expansions are used to construct curve estimates and variances conditional on a specific decomposition. Iterated expectation and variance formulas combine model-based conditional estimates across the distribution of decompositions. A bootstrap procedure is implemented to understand the uncertainty in principal component decomposition quantities. Our method compares favorably to competing approaches in simulation studies that include both densely and sparsely observed functions. We apply our method to sparse observations of CD4 cell counts and to dense white-matter tract profiles. Code for the analyses and simulations is publicly available, and our method is implemented in the R package refund on CRAN.
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影响因子：
2
作者：
Crainiceanu, Ciprian M.;Staicu, Ana-Maria;Ray, Shubankar;Punjabi, Naresh
通讯作者：
Punjabi, Naresh
影响因子：
5.7
作者：
Goldsmith, Jeff;Crainiceanu, Ciprian M.;Caffo, Brian S.;Reich, Daniel S.
通讯作者：
Reich, Daniel S.
影响因子：
1.1
作者：
Greven S;Crainiceanu C;Caffo B;Reich D
通讯作者：
Reich D
影响因子：
5
作者：
KASLOW, RA;OSTROW, DG;RINALDO, CR
通讯作者：
RINALDO, CR
影响因子：
1.9
作者：
RAO, CR
通讯作者：
RAO, CR