A considerable experimental effort is currently under way to test the persistent hints for oscillations due to an eV-scale sterile neutrino in the data of various reactor neutrino experiments. The assessment of the statistical significance of these hints is usually based on Wilks’ theorem, whereby the assumption is made that the log-likelihood is \(\chi ^2\)-distributed. However, it is well known that the preconditions for the validity of Wilks’ theorem are not fulfilled for neutrino oscillation experiments. In this work we derive a simple asymptotic form of the actual distribution of the log-likelihood based on reinterpreting the problem as fitting white Gaussian noise. From this formalism we show that, even in the absence of a sterile neutrino, the expectation value for the maximum likelihood estimate of the mixing angle remains non-zero with attendant large values of the log-likelihood. Our analytical results are then confirmed by numerical simulations of a toy reactor experiment. Finally, we apply this framework to the data of the Neutrino-4 experiment and show that the null hypothesis of no-oscillation is rejected at the 2.6 \(\sigma \) level, compared to 3.2 \(\sigma \) obtained under the assumption that Wilks’ theorem applies.

当前正在进行大量的实验工作，以测试各种反应堆中微子实验数据中由于eV级无菌中微子引起的振荡的持久提示。对这些提示的统计意义的评估通常基于威尔克斯定理，从而假设对数似然为\（\ chi ^ 2 \）-分散式。但是，众所周知，中微子振荡实验没有满足威尔克斯定理有效性的前提条件。在这项工作中，我们通过将问题重新解释为拟合高斯白噪声，得出对数似然率实际分布的简单渐近形式。从这种形式上，我们表明，即使在没有无菌中微子的情况下，混合角的最大似然估计的期望值也保持非零，并伴随着对数似然的大值。然后，我们的分析结果通过玩具反应堆实验的数值模拟得到证实。最后，我们将此框架应用于Neutrino-4实验的数据，并证明在2.6 \（\ sigma \）处拒绝无振荡的零假设。 级别，与在采用威尔克斯定理的假设下获得的3.2  \（\ sigma \）进行比较。