Titlebook: On the Estimation of Multiple Random Integrals and U-Statistics; Péter Major Book 2013 Springer-Verlag Berlin Heidelberg 2013 60H05, 60G60

OUTRE

,Vapnik–Červonenkis Classes and ,,-Dense Classes of Functions,In this chapter the most important notions and results will be presented about Vapnik–Červonenkis classes, and it will be explained how they help to show in some important cases that certain classes of functions are ..-dense. The classes of ..-dense classes played an important role in the previous chapter.

adequate-intake

The Completion of the Proof of Theorem 4.1,This chapter contains the proof of Proposition 6.2 with the help of a symmetrization argument, and this completes the proof of Theorem 4.1.

ESO

Some Results About ,-statistics,This chapter contains the proof of the Hoeffding decomposition theorem, an important result about .-statistics. It states that all .-statistics can be represented as a sum of degenerate .-statistics of different order. It also contains the proof of some important properties of the Hoeffding decomposition useful in later applications.

祝贺

熔岩

The Proof of Theorems 8.3, 8.5 and Example 8.7,In this chapter we prove the estimates on the distribution of a multiple Wiener–Itô integral or degenerate .-statistic formulated in Theorems 8.5 and 8.3, and also present the proof of Example 8.7. Beside this, we prove a multivariate version of Hoeffding’s inequality (Theorem 3.4).

存心

Disk199

Arthr-

A Symmetrization Argument,The proof of Propositions 15.3 and 15.4 applies some ideas similar to the argument in the proof of Proposition 7.3. But here some additional technical difficulties have to be overcome. Their study is the subject of the present chapter.

Limousine

Thyroid-Gland

An Overview of the Results and a Discussion of the Literature,I discuss briefly the problems investigated in this work, recall some basic results related to them, and also give some references. I also write about the background of these problems which may explain the motivation for their study. I list the remarks following the subsequent chapters in this work.