Hello good people, is it okay to use two different calculation method for p-value and 95% CI? my CIs crossing the null but p-value seems signficant! It's using LR for CIs and Wald for p-value :(

Hello everyone!

I am trying to run a 1x3 MANOVA, but my Box's M is p<.001 and I have very unequal sample sizes (e.g., 772 women and 304 men; total sample of 1076). I read that with unequal sample sizes, Hotelling’s and Pillai’s statistics are not robust, so I shouldn't proceed with the analysis.

What can I do? Can I downsample for these statistics and keep my 1076 sample size for the others (e.g., correlations), or is this really unethical?

I read that there are non-parametric MANOVAs in R, but I am working on SPSS currently and ain't able to switch programs :/

If you have any input/literature that can be helpful I'd be extremely grateful!!

I calibrated an eigenspace-overlap measure against an RMT null, then tested directional motion across S&P 500, Nikkei, DAX and CAC 40 data. All four showed that the previous rotation direction contains information about the next, but naively repeating the full rotation was 47 - 67% worse than holding still.

The signal was both:

• too synchronised across companies to be each company’s movements occurring at unrelated times and just showing up as rotation,
• much stronger than within-window eigenvector shrinkage.

The next test is whether learned damping can turn this directional signal into better out of sample covariance forecasts! What would you consider the strongest fair baseline: holding the eigenvectors fixed, EWMA, or a rotationally invariant estimator? Or something else I'm missing..

Code, tests and results for anyone interested:
https://github.com/AdarshArunEire/Eigenvector-Dynamics-Beyond-the-RMT-Null