Bugs report: IPCA.m about online_psp_matlab HOT 5 CLOSED

Dear @goodshawn12,

Thank you for pointing that out. We are gonna check it!

Cheers

from online_psp_matlab.

Dear @goodshawn12

thanks a lot again for pointing out these issues. We fixed Point 2 but we wonder why do you think Point 1 should be modified that way.

Thank you!

Andrea

from online_psp_matlab.

Dear Andrea,

From my understanding of the IPCA algorithm (specifically according to Eq. 11 in the Cardot & Degras, 2018), the Q matrix (the variable M in your code) should have a factor of (1 - f) for lambda matrix and f * (1-f) for outer-product of Uhatx, where in stationary case f = 1/ (n+1). Hence, when multiplying a factor to x, it appears to me that the factor of sqrt( f * (1-f) ) would produce the consistent result.

Please let me know if this makes sense to you.

Best,
Shawn

from online_psp_matlab.

Hi Shawn,

I think that the discrepancy is between the specific choices made in Cardot & Degras and other variants to the general method by Arora et al. , (page 3).

In particular, Cardot and Degras integrate eq (4) in their paper into this method for their covariance estimates, wheras Arora et al. do not seem to have such a recurrence integrated into eq (4) in their paper. In the implementation here, we were switching between the two papers and I believe settled on something in between.

In particular, I believe if you carry the factors through in this implementation, the ultimate matrix you compute eigenvectors of is a convex combination of the old lambda matrix and the new outer-product matrix, which I believe should also make sense.

Does this seem to explain the discrepancy? It does not answer the question "which is the best way of doing things?", and I do not know the answer to that but I do not anticipate any large differences except perhaps in the early iterations. Would you possibly be able to show a few of the example trajectories you computed with the different step rule? If there's a good empirical argument for using Cardot and Degras's steps in particular, we can certainly look at it.

Feel free to correct me if any of this seems incorrect or this does not seem like the source of the discrepancy!

Thanks,

Victor

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closing for lack of activity

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