Note on stability estimation in sequential hypothesis testing
Volume 40 / 2013
Applicationes Mathematicae 40 (2013), 109-116
MSC: Primary 62F03; Secondary 62L10.
DOI: 10.4064/am40-1-7
Abstract
We introduce a quantitative measure $\varDelta $ 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 $X\thicksim f_0$.
