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Note on stability estimation in sequential hypothesis testing

Volume 40 / 2013

E. Gordienko, J. Ruiz de Chávez, A. García 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 $X\thicksim f_0$.

Authors

  • E. GordienkoDepartamento de Matemáticas
    Universidad Autónoma Metropolitana-Iztapalapa
    San Rafael Atlixco 186
    Col. Vicentina
    C.P. 09340, Ciudad de México, D.F., México
    e-mail
  • J. Ruiz de ChávezDepartamento de Matemáticas
    Universidad Autónoma Metropolitana-Iztapalapa
    San Rafael Atlixco 186
    Col. Vicentina
    C.P. 09340, Ciudad de México, D.F., México
    e-mail
  • A. GarcíaDepartamento de Matemáticas
    Universidad Autónoma Metropolitana-Iztapalapa
    San Rafael Atlixco 186
    Col. Vicentina
    C.P. 09340, Ciudad de México, D.F., México
    e-mail

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