ABSTRACT
In this chapter we will present the basic tools needed for most of our subsequent chapters. These tools include empirical process theory and maximal inequalities, the delta method in infinite dimensional space, influence functions, functional derivatives, and Taylor type expansions in function space including the von Mises and Hoeffding expansions. These tools are essential for developing asymptotic inference for semiparametric models. Some of the proofs and references will be deferred to Appendix D.
