mGSFPCA: Estimate Functional Principal Components from Sparse Data
Implements functional principal component analysis (FPCA) for
univariate and multivariate sparse functional data. The package estimates
eigenfunctions, eigenvalues, and error variance simultaneously via maximum
likelihood estimation (MLE), using a spline basis representation of the
eigenfunctions. Orthonormality of the estimated eigenfunctions is enforced
through a modified Gram-Schmidt (MGS) orthogonalization procedure applied
iteratively during estimation, avoiding direct optimization over the Stiefel
manifold and improving numerical stability. The optimal number of basis
functions and principal components is selected via an Akaike Information
Criterion (AIC)-type criterion, supporting both a full grid-search strategy
and a computationally efficient sequential selection approach. Principal
component scores are estimated by conditional expectation, enabling
reconstruction of individual trajectories over the entire domain from sparse
observations. Pointwise confidence intervals for reconstructed trajectories
are also provided. Methods are described in Mbaka, Cao and Carey
(2026) <doi:10.48550/arXiv.2603.18833> and Mbaka and Carey (2026)
<doi:10.48550/arXiv.2603.19799>.
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[aut,
cre],
Michelle Carey