nonparametric regression

Here we’re interested in estimating

$$m(x)=\mathbb{E}[Y|X=x].$$

in a nonparametric setting (parametric versus nonparametric statistics), i.e., under no assumptions on the underlying data generation process. This is equivalent to writing

$$Y=m(X)+ϵ$$

where $ϵ$ has mean zero.

Methods for nonparametric regression:

• partitions and trees
• splines
• knn
• kernel regression

All of these are special cases of local polynomial regression.