OUTRE
发表于 2025-3-26 22:47:47
,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
发表于 2025-3-27 03:32:36
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
发表于 2025-3-27 05:21:02
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
发表于 2025-3-27 12:12:16
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熔岩
发表于 2025-3-27 13:36:09
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
发表于 2025-3-27 21:09:51
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Disk199
发表于 2025-3-28 01:54:05
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Arthr-
发表于 2025-3-28 05:41:09
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
发表于 2025-3-28 09:48:50
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Thyroid-Gland
发表于 2025-3-28 12:46:32
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.