Before revision:  The uniform rate of convergence and the nonstandard limiting distribution of the nonparametric threshold estimator are derived. The root-n consistency and the asymptotic normality of the regression slope parameter estimatorare also obtained.
After revision:  The uniform rate of convergence and the nonstandard limiting distribution of the nonparametric threshold estimator . We also obtain the root-n consistency and the asymptotic normality of the regression slope parameter estimatorare also obtained.