# Likelihood regularity conditions In [[Maximum likelihood estimation|maximum likelihood estimation]], we often assume that the likelihood fulfills some certain "regularity conditions", which give it some convenient qualities. These regularity conditions can be summarized as follows: 1. The likelihood has a unique maximum in the interior of the parameter space (as opposed to a boundary) 2. The likelihood can be well-approximated by a quadratic function near this maximum (aka we can use a Taylor expansion to approximate the likelihood) 3. Differentiation and integration can be exchanged for the likelihood These conditions allow the maximum likelihood estimator to have the desirable properties that it has. --- # References