Necessary and sufficient conditions for the conditional central limit theorem

By Jérôme Dedecker, F. Merlevède. 2002

98 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/adcaa3f0d40f208e5d1743370b792cc82005edb0

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Citations in the corpus

A new covariance inequality and applications (2003, background): “For further comments on Condition DR below, see also Dedecker and Merlevède (2002).”
STRONG INVARIANCE PRINCIPLES FOR DEPENDENT RANDOM VARIABLES (2007, result): “For recent contributions see Merlevède and Peligrad [38], Wu and Woodroofe [67] and Peligrad and Utev [40], where the central limit theory and weak convergence problems are considered.”
Central limit theorem for Markov processes with spectral gap in the Wasserstein metric (2011, background): “[8, 27, 35] and in [21] for continuous time processes.”
Recent advances in invariance principles for stationary sequences (2006, methodology): “The first result we would like to mention is in the spirit of Theorem 1 in Dedecker and Merlevède [10] and it is a version of Theorem 1 in Merlevède and Peligrad [42].”
On the Weak Invariance Principle for Non-Adapted Sequences under Projective Criteria (2007, background): “1 in Wang et al (2002) lies on page 134 between the equations (36) and (37) (the weak invariance principle (6) cannot follow from (36) and (37) only; to derive (6) from (37), the equality in (36) needs not only be true for any t ∈ [0, 1], but also for any finite dimensional marginals of the two proc”
CLT in functional linear regression models (2005, background): “Proof of Theorem 2 The proof of the rst part of Theorem 2 stems from the decomposition ( 11 ), Lemma 6, Proposition 2, the rst part of Proposition 3 and from the second result of Lemma 8.”
A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics (2013, methodology): “It turns out that a result by Dedecker and Merlevède [10] can also be proved by our Theorem 2.”
Central limit theorem for stationary linear processes (2005, unknown): “Thus, by Proposition 1 in [4], there exists a nonnegative variable η measurable with respect to I, such that E ∣∣E(p−1T 2 p |F0) − η∣∣ → 0 as p → ∞.”