Application of quasi-optimal weights to searches of anomalies. Statistical criteria for step-like anomalies in cumulative spectra

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.