We introduce a quantitative measure Δ of stability in optimal sequential testing of two simple hypotheses about a density of observations: f=f₀ versus f=f₁. The index Δ represents an additional cost paid when a stopping rule optimal for the pair (f₀,f₁) is applied to test the hypothesis f=f₀ versus a "perturbed alternative" f=f̃₁. An upper bound for Δ is established in terms of the total variation distance between f₁(X)/f₀(X) and f̃₁(X)/f₀(X) with X∼f₀.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am40-1-7,
author = {E. Gordienko and J. Ruiz de Ch\'avez and A. Garc\'\i a},
title = {Note on stability estimation in sequential hypothesis testing},
journal = {Applicationes Mathematicae},
volume = {40},
year = {2013},
pages = {109-116},
zbl = {1273.62190},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-1-7}
}
E. Gordienko; J. Ruiz de Chávez; A. García. Note on stability estimation in sequential hypothesis testing. Applicationes Mathematicae, Tome 40 (2013) pp. 109-116. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-1-7/