Note on stability estimation in sequential hypothesis testing
Tom 40 / 2013
Applicationes Mathematicae 40 (2013), 109-116
MSC: Primary 62F03; Secondary 62L10.
DOI: 10.4064/am40-1-7
Streszczenie
We introduce a quantitative measure of stability in optimal sequential testing of two simple hypotheses about a density of observations: f=f_0 versus f=f_1. The index \varDelta represents an additional cost paid when a stopping rule optimal for the pair (f_0,f_1) is applied to test the hypothesis f=f_0 versus a “perturbed alternative" f=\widetilde{f}_1. An upper bound for \Delta is established in terms of the total variation distance between f_1(X)/f_0(X) and \widetilde{f}_1(X)/f_0(X) with X\thicksim f_0.
