Bracketing Metric Entropy Rates and Empirical Central Limit Theorems for Function Classes of Besov- and Sobolev-Type

By Richard Nickl, B. M. Potscher. 2007

117 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9804c12fd0c06e3a969fbbfc14b1996200397faf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Numerical Analysis

Citations in the corpus

Policy Learning With Observational Data (2017, background): “16 15 See Nickl and P¨otscher (2007) for an argument that holds for arbitrary distributions P supported on [0 , 1] s .”
Adaptation on the space of finite signed measures (2008, background): “(16) For the ”bias term” we have, as in Lemma 4 in Giné and Nickl (2008a), for given f ∈ FBL with f̄(x) = f(−x), that”
Donsker-type theorems for nonparametric maximum likelihood estimators (2007, methodology): “Note first that the Hellinger-bracketing-metric entropy H[ ](ε, P t , ‖·‖2,λ) is of order ε−1/t where ε → 0 denotes the bracket size: since the functions in Pt are bounded from below by ζ , it follows from standard arguments that H[ ](ε, P t , ‖·‖2,λ| ) can be bounded (up to irrelevant constants) by”
The Balancing Act in Causal Inference (2021, background): “10To be more precise, this holds when both M and the related set {f(w, x) = wγipw(x)m(x) : m ∈ M} example, if M is the unit ball of a Sobolev space of functions on Rp with bounded derivatives of order s > p/2 (Nickl & Pötscher, 2007).”
GLOBAL UNIFORM RISK BOUNDS FOR WAVELET DECONVOLUTION ESTIMATORS (2011, background): “We will prove that (2−j/2δj )φj0 ∗ ηj has bounded quadratic variation by showing that it is contained in the (homogeneous) Besov space Ḃ 21 (R), which is sufficient, in view of the continuous embedding of Ḃ 21 (R) into the space V 2(R) of functions of quadratic variation (a result due to Peetre—see ”
Efficient Policy Learning (2017, background): “Thus, because the magnitude of the treatment 13See Nickl and Pötscher (2007) for an argument that holds for arbitrary distributions P supported on [0, 1]s.”
Uniform central limit theorems for kernel density estimators (2008, methodology): “, in the second paragraph of the proof of Theorem 2 in Nickl and Pötscher [20].”
On the uniform convergence of empirical norms and inner products, with application to causal inference (2013, background): “Entropy results for the supremum norm for such cases are in [21].”
On How Well Generative Adversarial Networks Learn Densities: Nonparametric and Parametric Results (2018, methodology): “For more details on Sobolev spaces, we refer to Nemirovski (2000); Tsybakov (2009); Nickl and Pötscher (2007).”