Titlebook: Self-Normalized Processes; Limit Theory and Sta Victor H. Peña,Tze Leung Lai,Qi-Man Shao Book 2009 Springer-Verlag Berlin Heidelberg 2009 B

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T. Figiel‘s integral representation, W.B. Johnson‘s factorization of operators, B. Maurey‘s isomorphism, and P. Jones‘ proof of the uniform approximation property. An entire chapter is devoted to the study of c978-3-7643-7345-0Series ISSN 0077-0507 Series E-ISSN 2297-0274

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Self-Normalized Empirical Processes and ,-StatisticsWhereas previous chapters have considered limit theorems for self-normalized sums of independent random variables, we extend sums to more general structures in this chapter, namely, self-normalized empirical processes and .-statistics. In particular, we extend the methods and results of Chaps. 6 and 7 to self-normalized .-statistics.

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978-3-642-09926-7Springer-Verlag Berlin Heidelberg 2009

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Self-Normalized Large Deviationsingredient of LDT is a finite moment generating function of . in a right neighborhood of the origin. Surprisingly, Shao (1997) shows that for self-normalized sums of the ., the LDT holds without any moment assumption on .. The main results and proofs of this self-normalized large deviation theory are given in Sect. 3.2.

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