  We discuss an "operational" approach to testing convex composite hypotheses
when the underlying distributions are heavy-tailed. It relies upon Euclidean
separation of convex sets and can be seen as an extension of the approach to
testing by convex optimization developed in [8, 12]. In particular, we show how
one can construct quasi-optimal testing procedures for families of
distributions which are majorated, in a certain precise sense, by a
sub-spherical symmetric one and study the relationship between tests based on
Euclidean separation and "potential-based tests." We apply the promoted
methodology in the problem of sequential detection and illustrate its practical
implementation in an application to sequential detection of changes in the
input of a dynamic system.
  [8] Goldenshluger, Alexander and Juditsky, Anatoli and Nemirovski, Arkadi,
Hypothesis testing by convex optimization, Electronic Journal of Statistics,9
(2):1645-1712, 2015. [12] Juditsky, Anatoli and Nemirovski, Arkadi, Hypothesis
testing via affine detectors, Electronic Journal of Statistics, 10:2204--2242,
2016.
