I am checking other's regression analysis work on a $p > n$ data. I can only see the results but not the process how he did it.
I believe he made mistakes. Since $p > n$, $X^T X$ is not full rank it is not invertible. So we cannot find the OLS coefficient.
However, I am not sure my reasoning is correct. I have not used linear algebra for a long time.
- No penalized methods involved.
- He used stepwise regression for variable selection. A new question: would such algorithm stop if number of variables in the model equal to the number of sample points?
- His goal is to find out which variables are important. Doesn't care about the prediction power.