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

It is demonstrated how the method of quasi-optimal weights can be applied to searches of anomalies in experimental data. As an example, a convenient statistical criterion is derived for step-like anomalies in cumulative β-decay spectra in the direct neutrino mass measurement experiments. It is almost as powerful as the locally most powerful one and appreciably excels the conventional χ2 and Kolmogorov–Smirnov tests. It is also compared with an ad hoc criterion of «pairwise correlations of neighbours»; the latter is seen to be less powerful even if more sensitive to more general anomalies. As a realistic example, the criteria are applied to the Troitsk-ν-mass data.