Bypassing the Likelihood

Abstract

Estimation based on the application of maximum likelihood methods can involve quite formidable difficulty in calculation of the joint distribution of the observations and sometimes even in differentiating the likelihood to obtain the corresponding estimating equations. Notable examples are the derivation of the restricted (or residual) (REML) estimating functions for dispersion parameters associated with linear models and the derivation of the maximum likelihood estimators of parameters in diffusion type models. In the former case both the derivation of the likelihood and its differentiation are less than straightforward while for the latter the Radon-Nikodym derivative calculations are a significant obstacle. Quasi-likelihood methods, however, allow such estimators (or estimating functions) to be obtained quite painlessly and under more general conditions. In this chapter we shall illustrate the power and simplicity of the approach through three quite different examples.