Data-Driven Bandwidth Selection for Recursive Kernel Density Estimators Under Double Truncation

Abstract

In this paper we proposed a data-driven bandwidth selection procedure of the recursive kernel density estimators under double truncation. We showed that, using the selected bandwidth and a special stepsize, the proposed recursive estimators outperform the nonrecursive one in terms of estimation error in many situations. We corroborated these theoretical results through simulation study. The proposed estimators are then applied to data on the luminosity of quasars in astronomy. We corroborated these theoretical results through simulation study, then, we applied the proposed estimators to data on the luminosity of quasars in astronomy.