A unified approach to a class of optimal selection problems with an unknown number of options
In the so-called secretary problem, if an unknown number, N, of options arrive at i.i.d. times with a known continuous distribution, then ignorance of how many options there are becomes almost irrelevant: The optimal rule for infinitely many options is shown to be minimax with respect to all possible distributions of N, nearly optimal whenever N is likely to be large, and formal Bayes against a non-informative prior. These results hold whatever the loss function.
scientific article; zbMATH DE number 3951700