Geodesic
A CLT for infinitely stratified estimators, with applications to debiased MLMC
Zeyu Zheng1 ; Peter W. Glynn1
1 Department of Management Science and Engineering, Stanford University, Stanford, California 94305
ESAIM. Proceedings, Tome 59 (2017), pp. 104-114 Cet article a éte moissonné depuis la source EDP Sciences

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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.
DOI : 10.1051/proc/201759104

Zeyu Zheng 1 ; Peter W. Glynn 1

1 Department of Management Science and Engineering, Stanford University, Stanford, California 94305 
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     author = {Zeyu Zheng and Peter W. Glynn},
     title = {A {CLT} for infinitely stratified estimators, with applications to debiased {MLMC}},
     journal = {ESAIM. Proceedings},
     pages = {104--114},
     year = {2017},
     volume = {59},
     doi = {10.1051/proc/201759104},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201759104/}
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Zeyu Zheng; Peter W. Glynn. A CLT for infinitely stratified estimators, with applications to debiased MLMC. ESAIM. Proceedings, Tome 59 (2017), pp. 104-114. doi: 10.1051/proc/201759104

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