Improving Kernel Density Estimation Near the Boundary

It is well-known that the application of kernel smoothing techniques becomes problematic when the unknown probability density function to be estimated has a bounded support. In fact, near the boundary, the kernel assigns positive weight to areas where the true density is zero, leading to a systematic bias. A classical solution is the reflection method, which presents some advantages but suffers from the presence of an additional bias term. The key novelty is the construction of a location-dependent mixture kernel embedded in the reflection framework, exploiting the higher order kernel theory. We also present some simulation results that support the effectiveness of our proposal.