High-dimensional Integration The computation of high-dimensional integrals is central to inferential statistics. Monte Carlo is usually the method of choice in this domain. The use of balanced sampling can be beneficial and using such ideas, our group has developed methods that have some degree of exactness for special integrands, are unbiased and highly efficient.
Minimax Methods When there is uncertainty about some aspect of a model, minimax estimators can be an attractive choice. In the context of robustness, for example, we may wish to estimate a statistical functional without exact knowledge of the underlying distribution. In this situation, minimax estimators offer a good compromise. We have studied such estimators in the polysampling setup.