Abstract
The chaining method is discussed, as well as the more general generic chaining method developed by Talagrand, see e.g. Talagrand (2005). This allows one to bound suprema of random processes. Concentration inequalities are refined probability inequalities, for instance for suprema of random processes, see e.g. Ledoux (2005), Boucheron et al. (2013) and Sect. 16.2 in this monograph. This chapter combines the two. A deviation inequality is obtained using (generic) chaining.
Keywords
- Talagrand
- Boucheron
- Generic Chaining
- Concentration Inequalities
- Probability Inequalities
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- 1.
See the footnote on the first page of Chap. 16
References
R. Dudley, The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Funct. Anal. 1, 290–330 (1967)
W. Hoeffding, Probability inequalities for sums of bounded variables. J. Am. Stat. Assoc. 58, 13–30 (1963)
M. Talagrand, The Generic Chaining (Springer, Heidelberg, 2005)
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van de Geer, S. (2016). Chaining Including Concentration. In: Estimation and Testing Under Sparsity. Lecture Notes in Mathematics(), vol 2159. Springer, Cham. https://doi.org/10.1007/978-3-319-32774-7_17
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DOI: https://doi.org/10.1007/978-3-319-32774-7_17
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