A frequentist analysis of solar neutrino data

We estimate 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. The Monte Carlo estimates are significantly smaller than the corresponding standard values. Using Neymanʹs method, we also calculate exact allowed regions with correct frequentist coverage assuming the standard least-squares estimator of the oscillation parameters. Our results 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 underestimated in the standard method.