ENH: OLS/WLS based on summary statistic, (cov_data)

[josef-pkt]

(I don't find an issue, but the idea is old.)

This is similar to #3570 but for the specific case of adding a model class for linear regression based on summary statistics like the covariance matrix of the data. As variation of this the summary statistic can be a matrix decomposition of exog.

This can include multivariate OLS.

One usecase is to use this with non-standard covariance matrix, e.g. a robust #3230 or penalized #3197 cov_data estimate.
For a sparse model it is not clear whether or when we need sparsified covariance or sparsified inverse covariance.

similar other multivariate methods can be based on "modified" covariance estimate.

[sunilk747]

Hello, I am new to this repo. I would like to work on this issue if nobody is working on this.

[josef-pkt]

Hi, AFAIK nobody is working on this

just a warning: this requires being familiar with the statsmodels models and results class structure.

The rough idea is to create a new model class that only takes the cross-product matrix of column_stacked (x, y), where x needs to have the constant as first column. as argument, and then replicate as much as possible of the RegressionResults class but only using the cross-product information.

[josef-pkt]

bump for 0.11
maybe something quick like OLSVectorized in special linear model #5382

Even having just minimal model and results classes would already be helpful for quick experimentation.
(and leave extension to using other linalg decomposition of the moment matrices for later.)

[josef-pkt]

bump again

after #8129 we can have outlier robust OLS based on cov

two possible interfaces

• moment matrices z.T z where z is column_stacked [exog, endog]
• centered moment cov(z) plus mean(z), cov(z) could be scatter/shape matrix for ols params

question is how do we compute cov_params, especially robust scale (residual variance), and possibly sandwiches?

One possibility for that would be to use only params for outlier-influence checks that check for more than a single outlier as the current outlier-influence diagnostic, i.e. allow higher breakdown point for outlier and influential point identification.
(I will open a separate issue)