Probability and moment inequalities for sums of weakly dependent random variables, with applications

By Paul Doukhan, Michael H. Neumann. 2007

112 citations recorded by the source corpus.

Doukhan and Louhichi [P. Doukhan, S. Louhichi, A new weak dependence condition and application to moment inequalities, Stochastic Process. Appl. 84 (1999) 313-342] introduced a new concept of weak dependence which is more general than mixing. Such conditions are particularly well suited for deriving estimates for the cumulants of sums of random variables. We employ such cumulant estimates to derive inequalities of Bernstein and Rosenthal type which both improve on previous results. Furthermore, we consider several classes of processes and show that they fulfill appropriate weak dependence conditions. We also sketch applications of our inequalities in probability and statistics.

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Citations in the corpus

Asset Allocation and Risk Assessment with Gross Exposure Constraints for Vast Portfolios (2008, background): “: Improving performance by constraining portfolio norms. Manuscript. [13] Donoho, D. L. and Elad, E. (2003). Maximal sparsity representation via l1 Minimization, Proc. Nat. Aca. Sci., 100, 2197-2202. [14] Doukhan, P. and Neumann, M.H. (2007). Probability and moment inequalities for sums of weakly de”
Vast Portfolio Selection with Gross-exposure Constraints (2012, unknown): “From Theorem 1 of Doukhan and Neumann (2007), under Condition 3, we have P (∥∥∥∥∥ n∑ t=1 ηt ∥∥∥∥∥ > √nx ) ≤ exp(−C min{x2, (√nx)c}), for some C > 0, where c = 1/(a + b + 2).”
NETS: Network estimation for time series (2019, unknown): “For such processes suitable Bernstein-type exponential inequalities for dependent processes apply (see, e.g., Bosq, 1996; Doukhan & Neumann, 2007; Merlevède, Peligrad, & Rio, 2011).”
Bernstein inequality and moderate deviations under strong mixing conditions (2012, methodology): “1 in Rio [18] using coupling coefficients, by Doukhan and Neumann [13] who used combinatorics techniques.”