Empirical Choice of the Block Size

Abstract

As we have seen in the earlier chapters, performance of block bootstrap methods critically depends on the block size. In this chapter, we describe the theoretical optimal block lengths for the estimation of various level-2 parameters and discuss the problem of choosing the optimal block sizes empirically. For definiteness, we restrict attention to the MBB method. Analogs of the block size estimation methods presented here can be defined for other block bootstrap methods. In Section 7.2, we describe the forms of the MSE-optimal block lengths for estimating the variance and the distribution function. In Section 7.3, we present a data-based method for choosing the optimal block length based on the subsampling method. This is based on the work of Hall, Horowitz and Jing (1995). A second method based on the Jackknife-After-Bootstrap (JAB) method is presented in Section 7.4. Numerical results on finite sample performance of these optimal block length selection rules are also given in the respective sections.