The Efficient Use of Function Minimization in Non-Linear Maximum-Likelihood Estimation

Abstract

Maximum‐likelihood estimation problems can be solved numerically using function minimization algorithms, but the amount of computing required and the accuracy of the results depend on the way the algorithms are used. Attention to the analytical properties of the model, to the relationship between the model and the data, and to descriptive properties of the data can greatly simplify the problem, sometimes providing a method of solution on a desk calculator. This paper describes how parameter transformation, sequential minimization and nested minimization can be used to solve particular problems. Applications to well‐known problems of distribution fitting, quantal responses and least‐squares curve fitting are described. The implications for computer programming are discussed.