Additive models

The most general nonparametric model is Yi= mu(X(1,i),X(2,i))+ error(i) where mu(X(1,i),X(2,i)) is completely arbitrary function of X(1,i) and X(2,i) . Instead of developing spline models with this level of generality we can instead use a simple model called an additive model: Y(i)= mu1(X(i,1))+ mu2(X(i,2))+error(i), thus one can just construct monomials and plus functions in X(i,1) and monomials and plus functions in X(i,2) to fit additive spline models easily.