Optimal Block Size for Variance Estimation by a Spatial Block Bootstrap Method

This paper considers the block selection problem for a block bootstrap variance estimator applied to spatial data on a regular grid. We develop precise formulae for the optimal block sizes that minimize the mean squared error of the bootstrap variance estimator. We then describe practical methods for estimating these spatial block sizes and prove the consistency of a block selection method by Hall, Horowitz and Jing (1995), originally introduced for time series. The spatial block bootstrap method is illustrated through data examples, and its performance is investigated through several simulation studies.