Decoupling: From Dependence to Independence

By Evarist Gin'e, Victor H. de la Peña. 1998

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Citations in the corpus

On the optimal estimation of probability measures in weak and strong topologies (2013, background): “llowing result is based on the standard chaining argument to obtain a bound on the expected suprema of the Rademacher chaos process of degree 2. While the reader can to refer to de la Pen˜a and Gin´e [7], Corollary 5.18, for a general result to bound the expected suprema of the Rademacher chaos proc”
Introduction to the non-asymptotic analysis of random matrices (2010, methodology): “To overcome this obstacle we shall use the decoupling technique of probability theory [22].”
Statistical inference on graphs (2006, background): “It is worth mentioning that Rn(g) is not a U-statistic (de la Peña and Giné [18]) stricto sensu, unless we assume the deterministic case Yn i j = η(Xi , Xj ).”
On consistency of kernel density estimators for randomly censored data: rates holding uniformly over adaptive intervals (2001, background): “for all n n0. Setting, for ease of notation, B 2 n := A 2 [(log e−1 n ) ∨ log log n)]/(nen) ,t he regularity of the sequence {en} implies that there exists d> 0s uch thatB2k dBn for all 2k−1 log n0. Then, by (2.17) and Montgomery-Smith’s [12] maximal inequality (see, e.g., de la Pena and Gine [ 6 ”
A Stochastic View of Optimal Regret through Minimax Duality (2009, background): “can view the sequence {Z ′ t} as being tangent to {Zt} (see [8]).”
Learning without Concentration (2014, unknown): “[5]).”
On local U-statistic processes and the estimation of densities of functions of several sample variables (2007, methodology): “This gives, by the entropy integral for Rademacher chaos of order k (de la Pena and Gine [7], Corollary 5.”
Moment inequalities for functions of independent random variables (2005, methodology): “Jorgensen’s inequality. In particular, we use inequality (1.2.5s) on page 10 in [ 13 ] with p = 1 and t = 0. Then we obtain”
Characterizations of joint distributions, copulas, information, dependence and decoupling, with applications to time series (2006, background): “The interested reader should consult de la Peña [14], de la Peña and Giné [15] and de la Peña and Lai [18] (a survey) for more on the subject.”
Rates of strong uniform consistency for multivariate kernel density estimators (2002, methodology): “It is worth mentioning at this point that the second tool we will require in the proofs below is Montgomery-Smith’s [10] maximal inequality (cf. de la Pe~ na and Gin e [ 3 ]):”
Kernel Choice and Classifiability for RKHS Embeddings of Probability Distributions (2009, methodology): “The proof is based on bounding the Rademacher chaos complexity of K, which can be understood as the U-process equivalent of Rademacher complexity [3].”
A simple adaptive estimator of the integrated square of a density (2008, background): “, de la Pena and Gine (1999), page 137) that the Hoeffding projections of R are 7t\R(x) = ER(x, Xi) - ER(X\,X2), tt2(R)(x, y) = R(x, y) - ER(x, Xj) - ER(y, X,) + ER(X}, X2), which induce the Hoeffding decomposition U^(R) - ER(Xx,X2) = 2UllX)(^R) + U{n2)(n2R), (2) where ?/?(1)(7ri R)=n~x Ya=i(^l #)(*”
Weighted uniform consistency of kernel density estimators (2004, background): “de la Peña and Giné (1999)), the stochastic boundedness of the sequence (2.”