  The statistical method of quasi-optimal weights can be used to derive
criteria for searches of anomalies. As an example we derive a convenient
statistical criterion for step-like anomalies in cumulative spectra such as
measured in the Troitsk-nu-mass, Mainz and KATRIN experiments. It is almost as
powerful as the locally most powerful one near the null hypothesis and
appreciably excels the conventional chi^2 and Kolmogorov-Smirnov tests. It is
also compared with an ad hoc criterion of {\guillemotleft}pairwise correlations
of neighbours{\guillemotright}; the latter is seen to be less powerful if more
sensitive to more general anomalies. As a realistic example, the criteria are
applied to the Troitsk-nu-mass data.
