Data-driven boundary estimation in deconvolution problems

Abstract

Estimation of the support of a density function is considered, when only a contaminated sample from the density is available. A kernel-based method has been proposed in the literature, where the authors study theoretical bias and variance of the estimator. Practical implementation issues of this method are considered here, which are a necessary supplement to the theoretical results to get to a data-driven method that is widely applicable. Two such practical data-driven procedures are proposed. Simulation results show that they perform well for a wide variety of densities (including quite difficult cases). The methods can also be applied for error-free data and as such also present data-drive..