Inference: Likelihood

Likelihood solutions for parametric survival models are described. These are relatively straightforward. The usual likelihood procedures for inference based on large samples can be applied. It is also possible to construct inference based on the derivative of the log-likelihood together with functions of Brownian motion. This approach is then close to that of the previous chapter. For the fully parametric approach the exponential model is particularly simple. The partial likelihood can be viewed in various ways: (1) as one term of a product, the other term containing little information on the unknown parameter, (2) as an approximation arising from use of the main theorem (Section 7.4), (3) as a marginal likelihood of the ranks, and (4) as a profile likelihood. Other techniques leaning on likelihood, such as conditioning on ancillary statistics as well as Bayesian inference, are highlighted.