if y=ax+n where y is a d-dimensional vector, a is a scalar (amplitude rescaling factor), and n is a d-dimensional vector drawn from a zero mean gaussian, what is the MLE of given x and y?

the way i see it, this is equivalent to minimizing the sum of squared errors:

, taking the derivative with respect to and setting it equal to zero i end up with . for some reason, this seems too simple, and intuitively, doesn't make a whole lot of sense. does this look right?

edit: n is drawn from a zero mean gaussian with vI covariance (v is scalar, I is the identity matrix).

i think its the same, except you're minimizing , so

edit 2: v cancels out,