Higher-Order Improvements of a Computationally Attractive k-Step Bootstrap for Extremum Estimators
证明k步自助法与标准自助法在高阶性质上等价，并给出极值估计量（如GMM、MLE）中自助法相比一阶渐近理论的高阶改进，适用于多种检验和置信区间。
This paper establishes the higher-order equivalence of the k-step bootstrap, introduced recently by Davidson and MacKinnon (1999), and the standard bootstrap. The k-step bootstrap is a very attractive alternative computationally to the standard bootstrap for statistics based on nonlinear extremum estimators, such as generalized method of moment and maximum likelihood estimators. The paper also extends results of Hall and Horowitz (1996) to provide new results regarding the higher-order improvements of the standard bootstrap and the k-step bootstrap for extremum estimators (compared to procedures based on first-order asymptotics). The results of the paper apply to Newton-Raphson (NR), default NR, line-search NR, and Gauss-Newton k-step bootstrap procedures. The results apply to the nonparametric iid bootstrap and nonoverlapping and overlapping block bootstraps. The results cover symmetric and equal-tailed two-sided t tests and confidence intervals, one-sided t tests and confidence intervals, Wald tests and confidence regions, and J tests of over-identifying restrictions.