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Note on stability estimation in sequential hypothesis testing. (English) Zbl 1273.62190

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
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