Georgia Institute of Technology College of Sciences

When considering smooth functionals of dependent data, block bootstrap methods have enjoyed considerable success in theory and application. For nonsmooth functionals of dependent data, such as sample quantiles, the theory is less well-developed. In this talk, I will present a general theory of consistency and optimality, in terms of achieving the fastest convergence rate, for block bootstrap distribution estimation for sample quantiles under mild strong mixing assumptions. The case of density estimation will also be discussed. In contrast to existing results, we study the block bootstrap for varying numbers of blocks. This corresponds to a hybrid between the subsampling bootstrap and the moving block bootstrap (MBB). Examples of `time series’ models illustrate the benefits of optimally choosing the number of blocks. This is joint work with Stephen M.S. Lee (University of Hong Kong) and Alastair Young (Imperial College London).