ABSTRACT
In this chapter we focus on robust statistical inference for the classical linear models. Section 2.2 first reminds some basic aspects of the classical theory of statistical inference. Section 2.3 outlines the concept of robustness. It discusses quantitative as well as qualitative aspects of robustness and also its local as well as global aspects. The minimax theory, scale-equivariance, and studentization are all important features related to robust statistical procedures. Their basic formulation is considered in Section 2.4. In the dissemination of the theory of robust statistical inference, we need to make use of basic results in probability theory as well as large sample theory. A systematic account of these results (mostly without proofs) is given in Section 2.5. Throughout this chapter, we emphasize the motivations (rather than the derivations). More technical derivations will be given in subsequent chapters.
