THE CONTINUITY OF THE LIMIT DISTRIBUTION IN THE PARAMETER OF INTEREST IS NOT ESSENTIAL FOR THE VALIDITY OF THE BOOTSTRAP
通过反例证明，在无漂移随机游走模型中，最小二乘估计量极限分布的不连续性并非自助法失效的根本原因，且估计量的收敛速度也不必在整个参数空间保持不变。
It is well known that the unrestricted bootstrap estimator of the slope parameter in the random walk model without drift converges to a random distribution. This bootstrap failure is commonly attributed to the discontinuity of the limit distribution of the least-squares estimator in the parameter of interest. We demonstrate by counterexample that this type of continuity is not essential for the validity of the bootstrap nor is it essential that the rate of convergence of the estimator remain constant over the whole parameter space.We thank Don Andrews, Shinichi Sakata, Jonathan Wright, and two anonymous referees for very helpful comments. The views expressed in this paper do not necessarily reflect those of the European Central Bank or its members.