  This paper investigates the nonparametric estimation of the functional
coefficients of the FBSDEs with random terminal time, including the local
constant and local linear estimators. We provide complete two-dimensional
asymptotics in both the time span and the sampling interval, allowing for the
precise characterization of their distribution. Moreover, the empirical
likelihood (EL) method to construct the data-driven confidence intervals for
these estimators is provided. Some numerical simulations investigate the
finite-sample properties of the estimators and compare the performance of the
EL method and the conventional method in constructing confidence intervals
based on asymptotic normality.
