A frequentist analysis of solar neutrino data

We calculate with Monte Carlo the goodness of fit and the confidence level of the standard allowed regions for the neutrino oscillation parameters obtained from the fit of solar neutrino data. We show that the values of the goodness of fit and of the confidence level of the allowed regions are significantly smaller than the standard ones. Using Neyman's method, we also calculate exact allowed regions with correct frequentist coverage. We show that the standard allowed region around the global minimum of the least-squares function is a reasonable approximation of the exact one, whereas the size of the other regions is dramatically underestimated in the standard method.