For a problem which I am working on at the moment, I'm interested in learning how the mean and variance of some response variable
y changes with two independent variables
x2 - i.e. for each coordinate in (
x2)-space I wish to have an estimate for $\mu_y$ and $\sigma_y$ in order to be able to approximately standardise new observations as they arrive.
I have enough domain knowledge to expect both the mean and variance of
y to vary smoothly across this space (plus I can likely place bounds on the gradient at any point), which I'd like to use to be able to deal with previously-unseen
x2 pairs as they arise.
What techniques would you suggest for such a problem?