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Abstract:
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In this talk, we introduce a new block bootstrap procedure for time series, called the extended tapered block bootstrap, to estimate the variance and approximate the sampling distribution for a large class of approximately linear statistics. Our proposal differs from the existing tapered block bootstrap in that the tapering is applied to the random weights in the bootstrapped empirical distribution. Under the framework of the smooth function model, we obtain asymptotic bias and variance expansions for the variance estimator and establish the consistency of 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. Simulation results will also be presented to illustrate theoretical findings.
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