Case Studies II

The examples of this section illustrate a variety of empirical process techniques applied in a statistical context. The first example is a continuation of the partly linear logistic regression example introduced in Chapter 1 and studied in some detail in Chapter 4. The issues addressed are somewhat technical, but they are also both instructive and necessary for securing the desired results. The second example utilizes empirical process results for independent but not identically distributed observations from Chapter 11 to address an issue in clinical trials. The third example applies Z-estimation theory for estimation and inference in the proportional odds regression model for right-censored survival data, while the fourth example considers hypothesis testing for the presence of a change-point in the regression model studied in Section 14.5.1. An interesting feature of this fourth example is that the model is partially unidentifiable under the null hypothesis of no change-point. The fifth example utilizes maximal inequalities (see Section 8.1) to establish asymptotic results for very high dimensional data sets which arise in gene microarray studies. These varied examples demonstrate how the empirical process methods of the previous chapters can be used to solve challenging and important problems in statistical inference.