Observations of neutrino oscillations have unambiguously proven that neutrinos have non-zero masses. Precision measurements of beta-decay kinematics represent the most promising model-independent approach to probing the extremely small absolute neutrino mass scale in a laboratory experiment.
Direct neutrino mass experiments have a long history dating back to the late 40s, and the development of experimental techniques has allowed to push the sensitivity to the level of 2 eV. Given this limit, all direct searches up to now have yielded values for mν2 which are compatible with zero. Moreover, with most best-fit estimates for the measured quantity mν2 lying in the unphysical range mν2 < 0 eV2, the best practice for analysing data and interpreting the results is not always obvious.
This talk will give an introduction to the measurement principle of beta-decay spectroscopy and expand on the statistical peculiarities connected to a physical parameter boundary. A brief review of past experiments and their approach in identifying systematic effects and treating statistical errors is given. Finally, a status update on the KArlsruhe TRitium Neutrino experiment is presented, which aims to push the neutrino mass sensitivity into the sub-eV regime by improving the statistical and systematic sensitivity of this measurement technique by two orders of magnitude.