I am trying to comprehend the proof of the Least Angle Regression algorithm and I am stuck at certain points. I would appreciate any help that I can get.
Let me set the stage: I am following the paper in the following link
On Page 8, in the paper, they make the following claim (restated in my own words).
The sign of the correlation of every predictor in the active set stays a constant.
Though I intuitively understand it I am trying to formally prove this claim.
I have some ideas, but none give me conclusive proof. For example if I end up proving that the step taken in the equi-angular direction is less than the least squares step then I am done. But I am not able to prove that either.
Can anyone help me?