I have two independent samples X and Y where $x_i \sim F$ and $y_i \sim G$. Two different estimators A and B map X to $x_0$ and Y to $y_0$ respectively. I'd like to compare $x_0$ and $y_0$. The method addressed in https://web.as.uky.edu/statistics/users/pbreheny/621/F12/notes/10-11.pdf isn't suitable as I have two different estimators.
What bootstrap hypothesis test should I use?