Introduction to Empirical Processes

The goal of Part II is to provide an in depth coverage of the basics of empirical process techniques which are useful in statistics. Chapter 6 presents preliminary mathematical background which provides a foundation for later technical development. The topics covered include metric spaces, outer expectations, linear operators and functional differentiation. The main topics overviewed in Chapter 2 of Part I will then be covered in greater depth, along with several additional topics, in Chapters 7 through 14. Part II finishes in Chapter 15 with several case studies. The main approach is to present the mathematical and statistical ideas in a logical, linear progression, and then to illustrate the application and integration of these ideas in the case study examples. The scaffolding provided by the overview, Part I, should enable the reader to maintain perspective during the sometimes rigorous developments of this section.