ABSTRACT
This chapter considers the computational requirements that arise in treating two kinds of nonlinear models. The first kind involves models for data whose means are smooth but nonlinear functions of the parameters; this is the classic example of nonlinear regression. The second kind are models for data which, despite possible linear structure, have likelihoods that are not quadratic in the parameters due to such factors as non-Gaussian errors, missing data, or dependence. The chapter deals with computational maximum likelihood as the context. It discusses several classes of statistical problems in which these computational methods play a prominent role: the so-called "computer-intensive" fitting techniques, estimation of missing data, and modeling time-series dependence. The chapter examines the basic features of maximum likelihood estimation. R. W. M. Wedderburn has introduced the notion of quasi-likelihood functions, which can be used for parameter estimation based on models defined only in terms of second-order properties.
