MATCHED-BLOCK BOOTSTRAP FOR DEPENDENT DATA

The block bootstrap for time series consists in randomly resampling bl ocks of consecutive values of the given data and aligning these blocks into a bootstrap sample. Here we suggest improving the performance of this method by aligning with higher likelihood those blocks which mat ch at their ends. This is achieved by resampling the blocks according to a Markov chain whose transitions depend on the data. The matching a lgorithms that we propose take some of the dependence structure of the data into account. They are based on a kernel estimate of the conditi onal lag one distribution or on a fitted autoregression of small order . Numerical and theoretical analyses in the case of estimating the var iance of the sample mean show that matching reduces bias and, perhaps unexpectedly, has relatively little effect on variance. Our theory ext ends to the case of smooth functions of a vector mean.