A Short Introduction To Nonparametric Curve Estimation

Some ideas about how basic aspects of nonparametric curve estimation can be introduced to students at a post secondary level will be discussed here. The idea of estimating population curves, like the density or the regression function, is studied from a nonparametric viewpoint. Starting from well-known estimators as the histogram or the regressogram, the discussion will then go to some of the smoothing methods developed in the last four decades, mainly focusing on the kernel density and regression estimators. Some ideas about the important problem of smoothing parameter selection will also be presented.