Estimation from k independent randomly truncated samples: application to neutrino energies

We investigate estimation and testing procedures for the k-sample problem where each of the populations is subject to random truncation by possibly different but known truncation functions. Particular attention is focused on the two sample case which is motivated from the following important application. Neutrinos were detected from Supernova 1987A at two sites: the 1MB detector in Ohio (eight neutrinos observed) and the Kamiokande II detector in Japan (twelve observed). Each detector has different "trigger efficiencies", the chance of observing the flash of light produced by the neutrino knocking an electron loose from an atom. Thus, we have two independent samples of randomly truncated data. We assume a normal model for some power transformation of the data with the same power for each sample. We estimate the parameters of this distribution by maximum likelihood and find confidence regions for the parameters. A Monte Carlo study investigates the properties of the maximum likelihood estimators for this eutrino example.The simulations Show that approximate likelihood-based confidence regions provide coverages much closer to the nominal level than the regions based on asymptotic normal-theory.