Module face 

FACE fast-sandwich covariance for sparse/irregular functional data.

This module adds the FACE (Fast Covariance Estimation) family that the R face / mfaces packages expose and that fdars previously lacked:

• face_covariance — a fast-sandwich covariance surface for sparse/irregular functional data.
• mface_covariance — its multivariate (mfaces) block extension for several simultaneously-observed sparse variables.
• face_trajectory — fitted continuous trajectories with pointwise confidence bands (a thin reuse of the shipped PACE FPCA path).

Divergence from refund::face

refund::face builds the covariance with a penalized tensor-product spline sandwich smoother (P-FACE). fdars instead sandwiches the existing kernel-smoothed sparse covariance (crate::irreg_fdata::cov_irreg) with a separable Gaussian smoother and projects the result to the nearest PSD matrix (a kernel-FACE, K-FACE). The two match by capability — a fast, symmetric, positive-semidefinite covariance surface for sparse data — not by exact internals. This keeps the estimator additive and dependency-free (it reuses cov_irreg and the Phase-37 sandwich smoother), per the milestone constraint.

Structs

MfaceCovResult

Multivariate FACE block covariance across several sparse variables.

Functions

face_covariance

FACE fast-sandwich covariance surface for sparse/irregular functional data.

face_trajectory

Fitted continuous trajectories with pointwise confidence bands for sparse functional data.

mface_covariance

Multivariate FACE (mfaces) block covariance across P >= 2 sparse variables.