Improving upon the effective sample size based on Godambe information for block likelihood inference

We consider the effective sample size, based on Godambe information, for block likelihood inference which is an attractive and computationally feasible alternative to full likelihood inference for large correlated datasets. With reference to a Gaussian random field having a constant mean, we explore how the choice of blocks impacts this effective sample size. This is done by introducing a column-wise blocking method which spreads out the spatial points within each block, instead of keeping them close together as the existing row-wise blocking method does. It is seen that column-wise blocking can lead to considerable gains in effective sample size and efficiency compared to row-wise blocking, while retaining computational simplicity. Analytical results in this direction are obtained under the AR (1) model. The insights so found facilitate the study of other one-dimensional correlation models as well as correlation models on a plane, where closed form expressions are intractable. Simulations are seen to provide support to our conclusions.