Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions

By E. Rio. 2009

128 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6403a1ecbc84d1a192ac870d79af451977cb90e6

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Citations in the corpus

Probability and moment inequalities under dependence (2013, background): “Rio (2009) showed a Rosenthal-type inequality for stationary processes: for 2 p ≤ 3, one has ∥Sn∥p ≤ cpn1/2σN + cpn1/p(∥X0∥p +∆1/2N +DN ), (2.1) where N = min{i : 2i ≥ n} and σN = ∥X0∥2 + 1 2 N−1∑ l=0 2−l/2∥E(S2l |F0)∥2, ∆N = N−1∑ l=0 2−2l/p∥E(S22l |F0)− E(S 2 2l)∥p/2, DN = N−1∑ l=0 2−l/p∥E(S2l…”
Inequalities and limit theorems for weakly dependent sequences (2013, methodology): “Either use Inequality (2.3) in Pinelis (1994) or adapt the proof of Theorem 2.5 to prove the inequality (4) below, given in Rio (2009): (4) ‖Sn‖2p ≤ ‖S0‖2p + (p− 1) n∑ k=1 ‖Xk‖2p. 3.”
Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples (2011, methodology): “This ends the proof of the inequality (27).”
Towards a general theory for nonlinear locally stationary processes (2017, result): “Using the projection operator Pj· := E[·|Fj]−E[·|Fj−1], we can bound moments of sums of ∂uX̃t(u) by moments of martingales which can then be bounded with results from Rio, E. (2009). It can be shown (similar to Wu, W.B. (2005), Theorem 1(i) and (ii)) that for some shift process Wt = Ht(Ft) with meas”
Oracle Inequalities and Optimal Inference under Group Sparsity (2010, background): “This constant is of the optimal order in m but larger than the one obtainable from the recent sharp moment inequality due to Rio [33].”