Corrected confidence bands for functional data using principal components.
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This article proposes a method for obtaining correct curve estimates by accounting for uncertainty in FPC decompositions, and applies this method to sparse observations of CD4 cell counts and to dense white-matter tract profiles.Abstract:
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.read more
Citations
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References
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Reference EntryDOI
Principal Component Analysis
TL;DR: Principal component analysis (PCA) as discussed by the authors replaces the p original variables by a smaller number, q, of derived variables, the principal components, which are linear combinations of the original variables.
Book
Analysis of longitudinal data
TL;DR: In this paper, a generalized linear model for longitudinal data and transition models for categorical data are presented. But the model is not suitable for categric data and time dependent covariates are not considered.
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MR diffusion tensor spectroscopy and imaging.
TL;DR: Once Deff is estimated from a series of NMR pulsed-gradient, spin-echo experiments, a tissue's three orthotropic axes can be determined and the effective diffusivities along these orthotropic directions are the eigenvalues of Deff.
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Diffusion tensor imaging: Concepts and applications
D. Le Bihan,J.-F. Mangin,Cyril Poupon,Chris A. Clark,Sabina Pappatà,Nicolas Molko,Hugues Chabriat +6 more
TL;DR: The concepts behind diffusion tensor imaging are reviewed and potential applications, including fiber tracking in the brain, which, in combination with functional MRI, might open a window on the important issue of connectivity.
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In vivo fiber tractography using DT-MRI data
TL;DR: Fiber tract trajectories in coherently organized brain white matter pathways were computed from in vivo diffusion tensor magnetic resonance imaging (DT‐MRI) data, and the method holds promise for elucidating architectural features in other fibrous tissues and ordered media.