A new covariance inequality and applications

By Jérôme Dedecker, Paul Doukhan. 2003

158 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6b0fd1f5969c5c9b9a8ee7265cb21aecbbbc8c30

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In Artificial Intelligence

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Citations in the corpus

Probability and moment inequalities for sums of weakly dependent random variables, with applications (2007, methodology): “(ii) Based on a Rosenthal-type inequality, Doukhan and Louhichi (1999) also proved an exponential inequality for Sn, however, with √ t instead of t(2) in the exponent.”
Inequalities and limit theorems for weakly dependent sequences (2013, methodology): “We refer to Dedecker and Doukhan (2003) for extensions of (a) and to Dedecker, Gouëzel and Merlevède (2010) for applications of (a) to Markov chains associated to intermittent maps (these chains fail to be strongly mixing in the sense of Rosenblatt).”
WEAKLY DEPENDENT CHAINS WITH INFINITE MEMORY (2007, background): “We give an appropriate condition on F (see (3.4) below) that leads to versions of the results of Dedecker and Doukhan [6] and Dedecker and Prieur [8] obtained under weak dependence.”
A simple integer-valued bilinear time series model (2006, methodology): “In the notation of [7], we will calculate θt = E[|st − s|].”
An exponential inequality under weak dependence (2006, background): “(ii) Alternative conditions which are more closely related to classical mixing concepts are proposed by Dedecker and Doukhan (2003).”
A Bernstein type inequality and moderate deviations for weakly dependent sequences (2009, methodology): “Applying Inequality (4.2) of Proposition 1 in Dedecker and Doukhan (2003), we derive that, for any positive k, |Cov(Wi,Wi+k)| ≤ 2 ∫ γ(Mi,Wi+k)/2 0 Q|Wi| ◦G|Wi+k|(u)du where γ(Mi,Wi+k) = ‖E(Wi+k|Mi) − E(Wi+k)‖1 ≤ τ(k) , since x 7→ ϕM(x) is 1-Lipschitz.”
New dependence coefficients. Examples and applications to statistics (2005, methodology): “Applying Proposition 4 in Dedecker and Doukhan (2003), we obtain that ‖Sn(h)− E(Sn(h))‖p ≤ ( 2p n∑ i=1 max i≤l≤n ∥∥∥Yi l∑ k=i E(Yk|Mi) ∥∥∥ p/2 )1/2 .”
Banded and tapered estimates for autocovariance matrices and the linear process bootstrap (2010, background): “4 in Dedecker and Doukhan (2003), kMk;nk4 kP0Ykk4 8 Xn j¼1 a2ij !”
On recursive estimation for time varying autoregressive processes (2005, methodology): “The following lemma is adapted from [9], Proposition 4.”
Recent advances in invariance principles for stationary sequences (2006, background): “Concerning the higher moments, we give the following result which is an extension to non-stationary sequences of Theorem 2.5 of Rio [61] and which is due to Dedecker and Doukhan [ 9 ].”