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

Abstract

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 outperforming 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 ( x i ) , max ( x i ) ] ) is used in their place, similar behaviour surfaces.