THE BOOTSTRAP IN THRESHOLD REGRESSION
开发了一种检验自助法在M估计中有效性的通用程序，应用于非连续阈值回归，发现非参数自助法对阈值点的推断不一致，并总结了文献中的补救方法。
This paper develops a general procedure to check the bootstrap validity in M -estimation. We apply the procedure in discontinuous threshold regression to show the inconsistency of the nonparametric bootstrap for inference on the threshold point. Especially, the conditional weak limit of the nonparametric bootstrap is shown not to exist. By comparing with two other boundaries in the literature, we show the fact that the threshold point is a boundary of the covariate that makes its bootstrap inference so different. The remedies to the bootstrap failure in the literature are summarized, and the nonparametric posterior interval is suggested by some simulation studies.