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Note on stability estimation in sequential hypothesis testing
E. Gordienko1 ; J. Ruiz de Chávez1 ; A. García1
1 Departamento de Matemáticas Universidad Autónoma Metropolitana-Iztapalapa San Rafael Atlixco 186 Col. Vicentina C.P. 09340, Ciudad de México, D.F., México
Applicationes Mathematicae, Tome 40 (2013) no. 1, pp. 109-116 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $X\thicksim f_0$.
DOI : 10.4064/am40-1-7
Keywords: introduce quantitative measure vardelta stability optimal sequential testing simple hypotheses about density observations versus index vardelta represents additional cost paid stopping rule optimal pair applied test hypothesis versus perturbed alternative widetilde upper bound delta established terms total variation distance between widetilde thicksim

E. Gordienko 1 ; J. Ruiz de Chávez 1 ; A. García 1

1 Departamento de Matemáticas Universidad Autónoma Metropolitana-Iztapalapa San Rafael Atlixco 186 Col. Vicentina C.P. 09340, Ciudad de México, D.F., México 
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E. Gordienko; J. Ruiz de Chávez; A. García. Note on stability estimation in sequential hypothesis testing. Applicationes Mathematicae, Tome 40 (2013) no. 1, pp. 109-116. doi: 10.4064/am40-1-7

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