Empirical Processes Indexed by Lipschitz Functions

By Evarist Gin'e, Joel C. Zinn. 1986

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Citations in the corpus

On the optimal estimation of probability measures in weak and strong topologies (2013, background): “…) and √ n ( P n ∗ K h − P ) in ℓ ∞ ( F BL ) holds only under a certain moment condition on P , i.e., R | x | 1+ γ d P ( x ) < ∞ for some γ > 0 (see [20, Theorem 2]) while no such condition on P is required to obtain the UCLT for the above processes in ℓ ∞ ( H ) though both · k F BL and · k F H…”
Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces (2005, unknown): “Acknowledgment: The authors thank M. Ledoux for his relevant comments and his interest during the preparation of this work, as well as providing Reference [ 16 ].”
Adaptation on the space of finite signed measures (2008, background): “The question whether (8) in Theorem 1 can be obtained for adaptive density estimators on R has been treated in several places in the literature.”
Donsker-type theorems for nonparametric maximum likelihood estimators (2007, background): “the general Donsker-theorem for empirical processes gives convergence at rate √ n of Pn to P in certain metrics metrizing the weak topology on P(�) ,s ee, e.g., [12,33], and also [ 14 ].”
Uniform central limit theorems for kernel density estimators (2008, background): “Theorem 2 in [12] for the Lipschitz case and also Theorems 4 and 6 in Nickl [17]).”
Bracketing Metric Entropy Rates and Empirical Central Limit Theorems for Function Classes of Besov- and Sobolev-Type (2007, result): “Remark 5 Extending results by Giné and Zinn [16, 17] and Arcones [4], van der Vaart [34] considers Lipschitz-type classes on R and obtains bounds for their L (P)bracketing metric entropy for r < ∞.”