An example with M=10 (basis functions) and r=5 (non-zero eigenvalues)
A simulated dataset as an example which corresponds to the "practical" case in the paper
prac is a list with six components (in the given order):
data matrix with three columns: column 1–ID, column 2–measurement, column 3–time.
true eigenfunctions: generated from cubic Bsplines with M=10 equally spaced knots.
true eigenvalues: first–1, second–0.66, third–0.52, fourth–0.44, fifth–0.38, others–zero.
true number of basis functions: M=10.
true dimension of the process: r=5.
true error standard deviation: 0.25.
mean curve of the process is zero; principal component scores and errors are all i.i.d N(0,1); there are 500 subjects, and each has 2~10 measurements uniformly distributed on [0,1]; in total there are 3018 measurements