A study of estimation in situations where we believe we have enough knowledge to model some features of the data parametrically, but are unwilling to assume anything for other features. Such models have arisen in a wide variety of contexts, particularly in economics, epidemiology and astrology. The complicated structure of these models typically requires us to consider nonlinear estimation procedures which often can only be implemented algorithmically. The theory of these procedures is necessarily based on asymptotic approximations.