I have some data that was collected by different sensors. I compute some statistics over this data, like the mean. I would like to get an idea of how much my results are sensitive to the particular sensors that I'm using. The reason is that more sensors may be added in the future and I would like to get some confidence that the results will hold then.
I have first thought of using a bootstrap approach, but instead of sampling from the data uniformly, I sample the sensors with replacement and form each bootstrap sample from the data that was collected by the selected sensors (if one sensor is selected twice, the related data is inserted twice into the sample). After that, I compute the 95% confidence interval for the mean of the resulting data samples.
I am not at all certain that this approach yields valid confidence intervals or even valid mean estimates because each sensor may have collected a different amount of data from the others and, since they are imperfect, they may have a different bias from one another, and thus may produce measurement that are not exactly identically distributed across sensors.
I've been looking for a method that could help me answer my original question. I've come across "block bootstrap", but I haven't yet found any resource to help me understand if it'd solve my problem. Any such resource or pointers to other methods that could help me would be appreciated.