4 Practical applications of bounded-influence tests

This chapter discusses the practical applications of bounded-influence tests. The robust versions of classical likelihood ratio, Wald or score tests, are now available in a general setting. They are more reliable than their classical counterparts—that is, they are not influenced by small deviations from the underlying model and can also be used as useful diagnostic tools to identify influential or outlying data points. The chapter illustrates their performance to show that they can be easily implemented in different practical situations. They can be used to robustly choose a model when the hypotheses are non-nested. That is when the model under the null hypothesis cannot be obtained as a particular or limiting case of the model under the alternative hypothesis. The approach followed is the approach based on the influence function. It is mainly concerned with the local robustness properties of tests. A parametric model is considered to study the effects of departures from the model on the testing procedures. The chapter also discusses robust testing in generalized linear models (or GLIM) and emphasizes the use of robust tests in logistic regression. As typical examples, the Food–Stamp data analyzed by Stefanski, Carroll, and Ruppert and the data introduced by Cormier, Magnan, and Morard in auditing is used.