ABSTRACT
Essential components of the statistician’s tool-kit involve procedures for dealing with likelihoods, and our objective in this chapter is to expand on the basic maximum-likelihood approach presented in Chapter 2. Classical statistical inference is basically made up of the three components: point estimation, interval estimation, where we construct confidence intervals or regions, and hypothesis testing. Point estimation by maximum-likelihood was introduced in Chapter 2. Now we consider all three aspects together. Standard references for this material are Cox and Hinkley (1974) and Silvey (1975), and in this chapter we shall outline the basic results. We shall not here provide the detail of the various regularity conditions which need to be satisfied in order for the results to hold. However, non-regular cases will be discussed in Section 5.8.
