5 problems

The observations are functional data observed at randomly distributed points, with $\underline{m}\to\infty$ and bandwidth $h\to 0$ satisfying $(\underline{m}h)^{-1}=o(1)$ and…

Approximate CV consistency conjecture. The approximate CV score defined by the paper is asymptotically consistent for the class of models considered there.

Functional-data efficient score conjecture. There exists an efficient score representation of the REML estimator in the functional-data problem.

Dense functional-data extension conjecture. Results derived for the Gaussian vectors, such as the efficient score representation, should carry over to the functional-data case with…

Optimal eigenfunction rate conjecture. The optimal rate for the $l_2$ risk of the eigenfunctions is of order