We know that many useful properties of the parametric distribution cannot be used when considering nonparametric distributions, thinking that in practice there are usually no such perfect parametric distributed data. Therefore it’s hard to construct control variate directly from the the raw data, instead researchers usually transform or map the raw data into some control variates that parameters such as mean and variance could be obtained. For example, the sequential nature methods based on change-point model and Mann-Whitney statistics (Hawkins and Deng(2010),Zhou and Zou(2010),Zou and Tsung (2010)), are commonly used. Even though they have abandoned many assumptions, but still here are some implicit assumptions which arise my interests:
What if the reference data is non iid?
How to decide the reference data size effectively as both control variate and control limit depend on it?
What if the the covariance but not only the mean has shifted?