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.
