In Li and Papanicolaou, Applied Mathematics & Optimization 86, 12 (2022), a key step is the determination of the diffusion matrix $\Sigma_0 = \Psi_0\Psi_0^T$ with $\Psi_0\in \mathbb{R}^{m\times (d+m)}$, eq. (2.2).
In numerical practice, how do you estimate this matrix? My question comes because the eigenportfolios $F$ have zero covariance by construction, so a diffusion matrix built from them is only diagonal, which is then problematic down the road. In their paper, the authors say they applied shrinkage, but it's not clear to me from which data they start from.
