Lots of great comments.  I think I have addressed most or all of them in my
cor_nearest branch.

Regarding this particular comment, I pushed the results into a new
FactoredPSDMatrix class and added a decorrelate method to it.

Decorrelation is the main application I know of for this.  It's used in
various high dimensional multivariate analysis method where the sample
correlation or covariance matrix is singular or badly conditioned, so you
can't decorrelate in the usual way.


On Sat, Apr 5, 2014 at 7:19 PM, Josef Perktold <notifications@github.com>wrote:

> In statsmodels/stats/correlation_tools.py:
>
> > +    rank : positive integer
> > +        The rank of the fitted factor structure
> > +
> > +    Returns
> > +    -------
> > +    k : positive real
> > +        The value of k in the fitted structure k*I + XX'
> > +    X : array_like
> > +        The value of X in the fitted structure k*I + XX'
> > +
> > +    Notes
> > +    -----
> > +    This routine is useful if one has an estimated correlation matrix
> > +    that is not SPD, and the ultimate goal is to estimate the inverse,
> > +    square root, or inverse square root of the true correlation
> > +    matrix. The factor structure allows these tasks to be performed
>
> Is there a recipe how to get the inverse or square root from this?
> square root should be obvious, but I don't see how to get the inverse.
>
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