Local linear estimators for reflected diffusions

In this paper, we investigate the nonparametric local linear estimator for the drift function of reflected stochastic differential equations based on the discretely observed process. Under certain regularity conditions, we prove the strong consistency and establish the asymptotic normality for our proposed estimator. We also propose the optimal bandwidth selector for the estimator and show that the estimator does not have a boundary effect. Simulation results demonstrate that our method is superior to the method proposed by Cholaquidis et al. [Stat. Sin. 2021, 31: 29–51]. We apply the EUR/USD currency exchange rate data to illustrate our theoretical results.