Timeline for How to properly "subtract" a known covariance component from a sample covariance? regression
Current License: CC BY-SA 4.0
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| Aug 30 at 8:53 | comment | added | Gilles Mordant | The sample size does not seem low, but I do not have a great feeling for it. In your case, I would start by computing the spectrum of the empirical covariance matrix that you have, compute a shrinked version of it (James--Stein; Dey and Srinivasan or else) and compare the two. It might help understand what to do next. Send me an email, I can provide code. | |
| Aug 29 at 16:57 | comment | added | Alex | Thank you! In my case I have ~10^5 observations. Do you know a rule of thumb for whether the sample size is big enough to avoid the biased spectrum issue? The Ledoit+Wolf method seems to be for estimating $\Sigma_X$, not doing the "subtraction". I will take a closer look and see if the method can be adapted to when you already know one part of the $X$ covariance. For your manifold optimization approach do you have a suggestion on a statistically well-motivated metric on sdps? Also, I am a bit afraid of trying to find a minimum of function in 1 million dimensions... is there a recommended way? | |
| Aug 29 at 9:28 | history | answered | Gilles Mordant | CC BY-SA 4.0 |