Weak Dependence: With Examples and Applications

By Jérôme Dedecker, Paul Doukhan, Gabriel Lang, León R. José Rafael, Sana Louhichi, Clémentine Prieur. 2007

336 citations recorded by the source corpus.

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In Artificial Intelligence

Citations in the corpus

A Kernel Test of Goodness of Fit (2016, background): “The two concepts required to derive the distribution of the test statistic are: τ -mixing (Dedecker et al., 2007; Leucht & Neumann, 2013), and V-statistics (Serfling, 1980).”
A Wild Bootstrap for Degenerate Kernel Tests (2014, background): “The main results of the paper are based around two concepts: τ -mixing [9], which describes the dependence within the time series, and V -statistics [26], which constitute our test statistics.”
Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples (2011, methodology): “We apply now the inequality (7) that has as effect the addition of a forth term, namely: n (∑n k=1 k ‖E0(Sk)‖p )p .”
Asymptotic results for the empirical process of stationary sequences (2009, neutral): “…Processes and their Applications ( ) – 5 the new weak dependence measures, such as τ (M, X ) = F X |M (t) − F X (t) 1 dt α(M, X ) = sup t∈R F X |M (t) − F X (t) 1 β(M, X ) = sup t∈R F X |M (t) − F X (t) 1 φ(M, X ) = sup t∈R F X |M (t) − F X (t) ∞ (see Dedecker et al. [22] [23] [24], Rio [56] [57]).”
QUASI‐LIKELIHOOD INFERENCE FOR NEGATIVE BINOMIAL TIME SERIES MODELS (2013, methodology): “This task is carried out by employing the notion of weak dependence; see Doukhan and Louhichi (1999), Dedecker et al. (2007) and Doukhan and Wintenberger (2008).”
Weak invariance principles for sums of dependent random functions (2013, background): “also [8]) solves this difficulty, but so far this concept has not been extended to variables in Hilbert spaces.”
Placebo inference on treatment effects when the number of clusters is small (2018, background): “Many other dependence structures are possible (see Dedecker et al., 2007, and the references therein), but this type of random field leads to particularly simple conditions.”
Mathematics of Two-Dimensional Turbulence (2012, result): “The SLLN and CLT discussed in this monograph can be derived from more general results of the book [DDL07], while the LIL can be obtained as a consequence of the invariance principles established in the recent papers [DM10] and [BMS11].”
Probability and moment inequalities under dependence (2013, background): “The latter quantities can be controlled by using various mixing coefficients in Bradley (2007), Rio (2000), and Dedecker et al. (2007).”
Komlós–Major–Tusnády approximation under dependence (2014, background): “There is a huge literature for central limit theorems and invariance principles for stationary processes; see, for example, the monographs of Ibragimov and Linnik (1971), Eberlein and Taqqu (1986), Bradley (2007), Dedecker et al. (2007) and Billingsley (1968), among others.”
Split invariance principles for stationary processes. (2011, background): “Several conditions of this kind have been found, in particular by the French school, see [10], [11], [12], [15], [36], [37].”
Estimation of Renyi Entropy and Mutual Information Based on Generalized Nearest-Neighbor Graphs (2010, background): “The third contribution is a strongly consistent estimator of R ´ enyi mutual information that is based on NN graphs and the empirical copula transformation (Dedecker et al., 2007).”
Extensions of some classical methods in change point analysis (2014, methodology): “For surveys we refer to Berkes and Horváth (2002), Bradley (2007), Dedecker et al. (2007) and Doukhan (1994).”