Boundary-adaptive kernel density estimation: the case of (near) uniform density

We consider nonparametric kernel estimation of density functions in the bounded-support setting having known support [a, b] using a boundary-adaptive kernel function and data-driven bandwidth selection, where a and b are finite and known prior to estimation. We observe, theoretically and in finite sample settings, that when bounds are known a priori this kernel approach is capable of out-performing even correctly specified parametric models, in the case of the uniform distribution. We demonstrate that this result has implications for modelling a range of densities other than the uniform case. Furthermore, when bounds [a, b] are unknown and the empirical support (i.e. [min(xi), max(xi)]) is used in their place, similar behaviour surfaces.

Automated summary

We propose a nonparametric kernel estimation method for density functions with known boundaries, using a boundary-adaptive kernel function and data-driven bandwidth selection. The results show that our approach can outperform correctly specified parametric models, even for the uniform distribution, when the bounds are known a priori. We also demonstrate the applicability of this method for modeling other densities when the bounds are unknown and the empirical support is used instead.