ABSTRACT
The likelihood function discussed in Chapter 3 allows us to compare two parameter
values with respect to the level of support that the sample provides for these values,
and hence to decide whether one parameter value has more support than another.
The objective of this chapter is to use the concept of likelihood to motivate a general
method of estimation, by identifying the most supported value out of all possible
values of the parameter. This is referred to as maximum likelihood estimation, and
can be used to provide estimates in situations where there is no obvious way to esti-
mate the parameter. We begin by discussing how to define the maximum likelihood
estimator followed by a discussion of the concept of statistical information, and its
use in providing standard errors and confidence intervals associated with maximum
likelihood estimates. We then consider properties of maximum likelihood estimation,
using the estimation concepts discussed in Chapter 2, and will see that it generally
provides the best possible approach to estimation. While maximum likelihood esti-
mation is the most important general approach, we will also discuss some alternative
methods that are useful in specific contexts, particularly the method of least squares
estimation. We then illustrate the concepts by continuing our disease incidence ex-
ample from Chapter 3.
