A CLT for Infinitely Stratified Estimators, with Applications to Debiased MLMCZ. Zheng and P. W. Glynn ESAIM: Proceedings and Surveys (B. Bouchard, E. Gobet and B. Jourdain, Editors), Vol. 59, p. 104-114, B. Bouchard, E. Gobet and B. Jourdain, Editors . This paper develops a general central limit theorem (CLT) for post-stratified Monte Carlo estimators with an associated infinite number of strata. In addition, consistency of the corresponding variance estimator is established in the same setting. With these results in hand, one can then construct asymptotically valid confidence interval procedures for such infinitely stratified estimators. We then illustrate our general theory, by applying it to the specific case of debiased multi-level Monte Carlo (MLMC) algorithms. This leads to the first asymptotically valid confidence interval procedure for such stratified debiased MLMC procedures. |