# Non-parametric confidence interval about the difference of means for unpaired data

Consider two samples ${(x_i)}_{i=1}^m$ and ${(y_i)}_{i=1}^n$. Assume that the $x_i$ are independent replicates from a distribution with expectation $\mu_X$ and similarly the $y_i$ are independent replicates from a distribution with expectation $\mu_Y$, and also assume that the two samples are independent. Is it possible to get a boostrap confidence interval about the difference of means $\mu_X-\mu_Y$ ? Or is there another nonparametric way to get such a confidence interval ?

EDIT : Oops - I've just seen this topic Confidence interval for the difference of two means using boot package in R Nevertheless I am interested in understanding why the method is correct. This is not a classical bootstrap procedure, isn't it ? Here we sample separately in each data sample. This is not like the classical bootstrap which is the case when there is only one data sample.