A practical approach to the error estimation of quasi-Monte Carlo integrations

There have been few studies on practical error estimation methods of quasi-Monte Carlo integrations. Recently, some theoretical works were developed by Owen to analyze the quasi-Monte Carlo integration error. However his method given by those works is complicated to be implemented and needs huge computational efforts, so it would be of some interest to investigate into a simple error estimation method. In this paper, we will use a simple method, and give some theoretical considerations on the errors given by these two methods. Numerical experiments are also reported.