Abstract: We propose a new block bootstrap procedure for time series, called the extended tapered block bootstrap, to estimate the variance and approximate the sampling distribution of a large class of approximately linear statistics. Our proposal differs from the existing tapered block bootstrap (Paparoditis and Politis (2001, 2002)) in that the tapering is applied to the random weights in the bootstrapped empirical distribution. Under the smooth function model, we obtain asymptotic bias and variance expansions for the variance estimator and establish the consistency of the distribution approximation. The extended tapered block bootstrap has wider applicability than the tapered block bootstrap, while preserving the favorable bias and mean squared error properties of the tapered block bootstrap over the moving block bootstrap. A small simulation study is performed to compare the finite-sample performance of the block-based bootstrap methods.
Key words and phrases: Block bootstrap, empirical measure, influence function, lag window estimator, tapering, variance estimation.