When the trend design matrix is identically zero, qr(Ftilde,0) may return a nonzero orthonormal vector Q with R=0. This is a valid QR factorization, but using Q to project Ytilde removes a component of Ytilde even though the column space of Ftilde is {0}. Therefore the QR-based ML variance estimate is not equivalent to the intended zero-mean likelihood in this degenerate trend case.
Could you provide a bit more context about where you encountered this issue?
In particular:
- Which module or function are you referring to?
- Do you have a minimal example that reproduces this behavior, or is this a theoretical concern based on your inspection of the implementation?
Best regards,
Styfen