Optimum Block Size in Separate Block Bootstrap To Estimate the Variance of Sample Mean For Lattice Data

The statistical analysis of spatial data is usually done under gaussian assumption for the underlying random field model. when this assumption is not satisfied, block bootstrap methods can be used to analyze spatial data. one of the crucial problems in this setting is specifying the block sizes. in this paper, we present asymptotic optimal block size for separate block bootstrap to estimate the variance of sample mean for spatial lattice data, using minimization of asymptotic mean square error of the estimator. further, an empirical method has been proposed to determine the optimal block size. also the optimality of the empirical estimate of block size has been considered numerically in a simulation study.