Block Bootstrap for the Empirical Process of Long‐Range Dependent Data

We consider the bootstrapped empirical process of long‐range dependent data. It is shown that this process converges to a semi‐degenerate limit, where the random part of this limit is always Gaussian. Thus the bootstrap might fail when the original empirical process accomplishes a noncentral limit theorem. However, even in this case our results can be used to estimate a nuisance parameter that appears in the limit of many nonparametric tests under long memory. Moreover, we develop a new resampling procedure for goodness‐of‐fit tests and a test for monotonicity of transformations.