Gordienko, E.; Ruiz De Chávez, J.; García, A. Note on stability estimation in sequential hypothesis testing. (English) Zbl 1273.62190 Appl. Math. 40, No. 1, 109-116 (2013). Summary: 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 \(X\thicksim f_0\). MSC: 62L10 Sequential statistical analysis 62G07 Density estimation Keywords:uncertainty about hypothesis; stability index; stability inequality PDFBibTeX XMLCite \textit{E. Gordienko} et al., Appl. Math. 40, No. 1, 109--116 (2013; Zbl 1273.62190) Full Text: DOI