Optimal bandwidth selection for local linear estimation of discontinuity in density

- A new bandwidth selection rule for estimating functions of the discontinuity in the density is proposed.
- The rule selects different bandwidths for both sides of the discontinuity and yields smaller asymptotic MSE than currently popular methods.
- A simulation study demonstrates the advantage of the proposed bandwidth selection rule.
- An empirical example illustrates the practical usefulness of our bandwidth selection rule.

We derive an optimal bandwidth selection rule for estimating a function of two one-sided limits of the probability density function at two cut-off points by the local linear estimation method. Our rule follows Arai and Ichimura (2015, AI, hereafter)'s principle and selects two bandwidths simultaneously, one for each cut-off point. Simulation results are presented. We also illustrate the usefulness of the method in an empirical application.