Simple and effective boundary correction for kernel densities and regression with an application to the world income and Engel curve estimation

In both nonparametric density estimation and regression, the so-called boundary effects, i.e. the bias and variance increase due to one sided data information, can be quite serious. For estimation performed on transformed variables this problem can easily get boosted and may distort substantially the final estimates, and consequently the conclusions. After a brief review of some existing methods a new, straightforward and very simple boundary correction is proposed, applying local bandwidth variation at the boundaries. The statistical behavior is discussed and the performance for density and regression estimation is studied for small and moderate sample sizes. In a simulation study this method is shown to perform very well. Furthermore, it appears to be excellent for estimating the world income distribution, and Engel curves in economics.