This paper establishes the higher-order equivalence of the k-step bootstrap, introduced recently by Davidson and MacKinnon (1999a), and the standard bootstrap. The k-step bootstrap is a very attractive alternative computationally to the standard bootstrap for statistics based on nonlinear...

It is well known that a one-step scoring estimator that starts from any N^{1/2}-consistent estimator has the same first-order asymptotic efficiency as the maximum likelihood estimator. This paper extends this result to k-step estimators and test statistics for k = 1, higher-order asymptotic...

This paper provides bounds on the errors in coverage probabilities of maximum likelihood-based, percentile-t, parametric bootstrap confidence intervals for Markov time series processes. These bounds show that the parametric bootstrap for Markov time series provides higher-order improvements...