New dependence coefficients. Examples and applications to statistics

By Jérôme Dedecker, Clémentine Prieur. 2005

211 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

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Citations in the corpus

Asymptotic theory for stationary processes (2011, background): “Recently Doukhan and Louhichi (1999) and Dedecker and Prieur (2005) have proposed some new types of dependence measures which in a certain degree overcome some drawbacks of strong mixing conditions.”
Probability and moment inequalities for sums of weakly dependent random variables, with applications (2007, background): “(a) If ψ(Lip g1,Lip g2, u, v) = vLip g2, then the sequence is called θ-dependent (see Doukhan and Louhichi (1999) and Dedecker and Doukhan (2003)) and we shall always denote r = θr.”
Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples (2011, methodology): “Starting from (14) and using (11) and (15) combined with Markov’s inequality, Inequality (9) of Proposition 5 follows.”
WEAKLY DEPENDENT CHAINS WITH INFINITE MEMORY (2007, methodology): “An easy way to calculate this coecient is based on a coupling argument (see [ 8 ] for details); assume that the probability space ( ,A) is rich enough, then there exists X distributed as X, independent of M, and such that (M,X) = EkX X k; the relation (M,X) EkX X k always holds.”
On the Weak Invariance Principle for Non-Adapted Sequences under Projective Criteria (2007, background): “For such maps, Dedecker and Prieur (2005) have proved that the coe(cid:14)cients (cid:30) ( k ) of the Markov chain , where W is a standard Brownian motion and This result seems to be new, although these dynamical systems have been widely studied.”
An empirical central limit theorem for dependent sequences (2007, methodology): “Using the same arguments as in Lemma 2 of Dedecker and Prieur (2005), the inequality (5.1) follows.”
Degenerate U- and V-statistics under weak dependence : Asymptotic theory and bootstrap consistency (2012, background): “…U - and V -type statistics, that is, nUn = 1 n n∑ j=1 ∑ k =j h(Xj ,Xk) and nVn = 1 n n∑ j,k=1 h(Xj ,Xk), with h: Rd × Rd → R symmetric and ∫ Rd h(x, y)PX(dx) = 0,∀y ∈ Rd, can be derived by using a spectral decomposition of the kernel, h(x, y) = ∑∞k=1 λk k(x) k(y), which holds true in the L2-sense.”