Avoiding the Likelihood

For the estimation of a finite dimensional parameter in a stochastic model it has become increasingly clear that it is usually possible to replace likelihood based techniques by quasi-likelihood alternatives in which only assumptions about means and covariances are made in order to obtain estimators.If it is available, the likelihood does provide a basis for benchmarking of alternative approaches but not more than that.The challenge is to see whether everything that can be done via likelihoods has a corresponding quasi-likelihood approach from which the likelihood based results can be recovered, if they are available.It is conjectured that this is the case.In this paper, various illustrations are sketched of avoiding the likelihood in contexts where alternative approaches have not been obvious.