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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