# Nonparametric estimation of regression function: kernel estimation vs series estimation

I am working on a small research project trying to estimate regression function nonparametrically when I have only one regressor. Basically, I am trying to estimate the regression function $$r(x)=E[Y∣X=x]$$ when I have i.i.d. pairs $(X_i,Y_i)$, $i=1,\ldots,n$.

I looked through the literature and I found that there are two main nonparametric techniques employed:

• using kernels
• series estimation using polynomials

My questions are:

• Are there any any rules of thumb that I shall use when selecting one of these nonparametric procedures?
• Does either of the above two approaches have some well known statistical or approximation advantages over the other?

(a) Outliers : if you have many outliers in your dataset, it is probably better to use the kernel method as only the local average at a particular outlier point is influenced by that outlier. In comparison, if you would use a series method, that particular outlier influences a whole function (e.g. the coefficient for your $x^2$).