ABSTRACT
In Chapter 2 we discussed parametric statistical models, and considered desirable
properties of estimators of the unknown parameter. While we considered a number
of criteria by which a given estimator can be judged, and discussed some particular
estimators appropriate for specific models, we did not discuss approaches to identify-
ing estimators in the first place. In this chapter we introduce the concept of likelihood,
which is the basis of the most important general approach to parameter estimation.
Our primary objective in this chapter is to present likelihood as a tool for identifying
the level of support that the observed data provide for particular values of the un-
known parameter. This will include a discussion of the likelihood function, together
with the idea of data reduction and the concept of sufficiency. After a discussion of
various extensions to multiple parameter contexts, the concepts will be illustrated
using an extended example on disease incidence rates. The likelihood function as a
tool for deriving estimation procedures will then be taken up in Chapter 4.
