# Comparing bins (quintiles, deciles) based of $R^2$s from multivariate regression

I have a multivariate linear model:

$$\mathbf{Y} = \mathbf{X}\mathbf{B} + \mathbf{U}$$

where the matrix $$\mathbf{Y}$$ represents stock returns, the design matrix is constituted by some explanatory macro variables. Stocks are grouped into two disjoint set, say A and B, and I am interested to see how they react to the covariates in $$\mathbf{X}$$.

If I split the multivariate model into the equivalent multiple regressions relative to each i-th share and set some fitting measure, say adjusted R2, I might cluster the R2's in deciles and test if each R2 in each decile of A is better/worse of each R2 in the same decile of B, or perhaps consider the average R2 per decile.

The idea of using quantile to compare groups, while simple, is used by some well-known scholar, check here for a quintile (not decile) approach: papers.ssrn.com/sol3/papers.cfm?abstract_id=1720139

I am thinking of using a quintile regression. If is identify the group A/B as a dummy, I might think to see with a plot how different are the group A and B at any chosen return quantile. The problem is that I normally see quantile regressions applied cross sectionally and here I have also time.

Is there an established way to apply a multivariate quantile regression?

• Sure, have a look at the package linked to in this answer – user603 Mar 31 '15 at 10:50
• "Quantile regression" is a well established statistical method to solve e.g. L1 optimization problems. The title is thus rather misleading. – Michael M Mar 31 '15 at 18:26
• Tried to improve the title, not sure how successfully, but at least the misleading part of quantile regression is gone. – Richard Hardy Sep 5 at 14:23