Coupling for τ-Dependent Sequences and Applications

By Jérôme Dedecker, Clémentine Prieur. 2004

122 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/af8c0efc3281238fcb2d8a5cd07674616c41e04f

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Citations in the corpus

An exponential inequality under weak dependence (2006, methodology): “(ii) Dedecker and Prieur (2004) proved a Bennett inequality for weakly dependent random variables.”
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].”
Asymptotic results for the empirical process of stationary sequences (2009, unknown): “…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]).”
STRONG INVARIANCE PRINCIPLES FOR DEPENDENT RANDOM VARIABLES (2007, background): “Motivated by the usefulness of such approximation scheme, researchers have established many results concerning mixingales and strongly mixing processes of various types; see Berkes and Philipp [4], Bradley [6], Eberlein [17], Shao [51], Rio [48], Lin and Lu [35], Dedecker and Prieur [13] and Philipp”
Strong approximation for a class of stationary processes (2009, unknown): “For dependent random variables, see [2,3,9,26,23,17,22,7,6].”
New dependence coefficients. Examples and applications to statistics (2005, methodology): “Then, using recent results of Rio (1996, 2000b), Collet et al. (2002) and Dedecker and Prieur (2003), we obtain a Berry-Esseen bound, a concentration inequality for Lipschitz functions, and a functional law of the iterated logarithm for partial sums.”
Inequalities and limit theorems for weakly dependent sequences (2013, background): “We refer to Doukhan and Surgailis (1998), Louhichi (2000), Dehling, Durieu and Volný (2009) and Dedecker (2010) for other types of dependence.”
Probability and moment inequalities for sums of weakly dependent random variables, with applications (2007, methodology): “A first exponential inequality was obtained in Doukhan and Louhichi (1999), a Bennett inequality in Dedecker and Prieur (2004), and a Bernstein-type inequality in Kallabis and Neumann (2006).”
A Bernstein type inequality and moderate deviations for weakly dependent sequences (2009, background): “In order to cover a larger class of examples we shall also consider less restrictive coefficients of weak dependence, such as the τ -mixing coefficients defined in Dedecker and Prieur (2004) (see Section 2 for the definition of these coefficients).”
Bernstein inequality and moderate deviations under strong mixing conditions (2012, background): “Corollary 5 Let (Xj)j�1 be as in Theorem 4. Suppose in addition that the sequence is L2 stationary and �2n ! 1. Then, limn!1 �2n=n = �2 > 0 and for all positive sequences an satisfying ( 10 ), (n 1=2Sn)n�1 satis…es (9) with the good rate function I(t) = t2=(2�2).”