Dependence concepts and selection criteria for lattice rules

Quasi-Monte carlo;Variance Reduction;Lattice Rule;Statistics

Taniguchi, Yoshihiro

University of Waterloo

关键词: Quasi-Monte carlo;    Variance Reduction;    Lattice Rule;    Statistics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/8205/3/Taniguchi_Yoshihiro.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Lemieux recently proposed a new approach that studies randomized quasi-Monte Carlothrough dependency concepts. By analyzing the dependency structure of a rank-1 lattice,Lemieux proposed a copula-based criterion with which we can find a ;;good generator” forthe lattice. One drawback of the criterion is that it assumes that a given function can bewell approximated by a bilinear function. It is not clear if this assumption holds in general.In this thesis, we assess the validity and robustness of the copula-based criterion. We dothis by working with bilinear functions, some practical problems such as Asian option pricing, and perfectly non-bilinear functions. We use the quasi-regression technique to studyhow bilinear a given function is. Beside assessing the validity of the bilinear assumption,we proposed the bilinear regression based criterion which combines the quasi-regression and the copula-based criterion. We extensively test the two criteriaby comparing them to other well known criteria, such as the spectral test through numerical experiments. Wefind that the copula criterion can reduce the error size by a factor of 2 when the functionis bilinear. We also find that the copula-based criterion shows competitive results evenwhen a given function does not satisfy the bilinear assumption. We also see that our newly introduced BR criterion is competitive compared to well-known criteria.