# [R] slightly OT: constrained least-squares estimation in a decomvolution model

Ranjan Maitra maitra at iastate.edu
Tue May 15 05:42:32 CEST 2007

Dear colleagues,

This is not strictly a R question, but more a methodology-related question.

I have the following linear model:   Y = X\beta + e.

Pretty standard stuff, but additionally, X is square, symmetric circulant. So, the LS estimate for \beta is given by just deconvolving Y with the inverse of X, and can be done using 1-d discrete convolution.

Now, suppose that I also add in the constraint that some of the \beta's are zero. Is it still possible to still use the convolution property (and the fact that the whole X matrix is circulant, symmetric) in some way?

This is important in my application, because discrete convolution is what makes the LS estimate of \beta able to be computed and I have to do it several times.

Any ideas or pointers on how to handle this? Has anyone dealt with this, in R or elsewhere?

Many thanks and best wishes,
Ranjan