2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130482We formulate two types of extension of the large deviation theory initiated by Bahadur in a non-regular setting. One can be regarded as a bound of the point estimation, the other can be regarded as the limit of a bound of the interval estimation. Both coincide in the regular case, but do not necessarily coincide in a non-regular case. Using the limits of relative Renyi entropies, we derive their upper bounds and give a necessary and sufficient condition for the coincidence of the two upper bounds. We also show the attainability of these two bounds in several non-regular location shift families.ProbabilityStatistics Theorytext