Justification of stratified bootstrap

[e-pet]

Hi there,

less of a feature request and more of a question - or, at most, a documentation request.

I am trying to understand whether or why stratified bootstrapping is a valid method to obtain CIs. (Not a statistician here.) I have understood that the standard bootstrap is proven to approximate a valid CI under certain assumptions, but I can for the life of me not find any reference discussing or showing that this is still true for y-stratified sampling. Intuitively, it feels like this approach should be underestimating the width of the CI since we're keeping a core property of the test set (the class ratio) fixed. Is this not the case? Could you point out any references that discuss this, or provide an argument for why this is a valid method? (I looked through the pROC paper but there it is only stated that stratified sampling is used, with no further discussion or justification of this choice. The cited references also don't seem to discuss this, or did I overlook something?) Sorry, probably a trivial question for a statistician...

Thank you for an excellent package in any case!

[xrobin]

Isn't there anything in Efron B. & Tibshirani R. J., (1993). An Introduction to the Bootstrap Chapman & Hall., New
York, London? That was my main reference for bootstrap writing the pROC package.
https://books.google.ch/books/about/An_Introduction_to_the_Bootstrap.html?id=MWC1DwAAQBAJ&source=kp_book_description&redir_esc=y

[e-pet]

I don't have access to that right now; ordered it and will report back once it arrives and I have had some time to have a look. ;-)