Uniform Central Limit Theorems

By A. van der Vaart. 2001

688 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/54f3303896fcdfe8a9d97d401e82bce0756efe25

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Citations in the corpus

Specification Tests of Parametric Dynamic Conditional Quantiles (2010, neutral): “, Dudley (1999, p. 94), or Denition 1.3.3 in van der Vaart and Wellner (1996). Since is generic, =) is indeed weak convergence on compacta.”
Monte Carlo Maximum Likelihood Estimation for Discretely Observed Diffusion Processes (2009, background): “, form a stationary (not necessarily ergodic) stochastic process; see, for example, [13, 15, 22, 33].”
Ranking the Best Instances (2006, background): “Remark 6 (ON THE COMPLEXITY ASSUMPTION) On the terminology of major sets and major classes, we refer to Dudley (1999). In the proof, we need to control empirical processes indexed by sets of the form {x : s(x) ≥ t} or {x : s(x) ≤ t}.”
Rejoinder: Local Rademacher complexities and oracle inequalities in risk minimization (2006, background): “Many other useful bounds on expected suprema of empirical and Rademacher processes (in particular, in terms of bracketing numbers) can be found in [47] and [16].”
Consistency of spectral clustering (2008, background): “Finally, to see the non-negativity of the eigenvalues, observe that if we consider the operator U n as an operator on L 2 ( P n ) we have Thus, U is a nonnegative operator on L 2 ( P n ) and as such only has a non-negative eigenvalues.”
Estimation of a k-monotone density: limit distribution theory and the Spline connection (2005, neutral): “By Dudley [10], Theorem 2.”
Limit theorems for empirical processes of cluster functionals (2009, background): “1] and, hence, also Ck is a VC-class with index bounded by 2k+1 [Dudley (1999), Theorem 4.2.3]. By van der Vaart and Wellner [(1996), Theorem 2.”
Sequential complexities and uniform martingale laws of large numbers (2015, background): “The proof of Theorem 2 requires more work than the classical symmetrization proof [11, 18] due to the non-i.”
Rates of strong uniform consistency for multivariate kernel density estimators (2002, neutral): “4 of Dudley [4] because the family of sets {{ (s, u): p ( (t − s)/h,u) φ(u)}: t ∈ R, h > 0}”
Gaussian approximation of suprema of empirical processes (2012, background): “3, and [19], Chapter 4, for examples where the uniform entropy integral can be suitably bounded.”
Adaptive estimation of a distribution function and its density in sup-norm loss by wavelet and spline projections (2008, methodology): “For the following central limit theorem, we denote by ∞(R) convergence in law for samplebounded processes in the Banach space of bounded functions on R, and by GP the usual P Brownian bridge (for example, Chapter 3 in [8]).”
Topological complexity of smooth random functions (2011, background): “5 Actually, d is only a pseudo-metric, since although it satisfies all the other demands of a metric, d(s, t) = 0 does not necessarily imply s = t. 2.5 The Basic Theory of Gaussian Fields 27 Here then is the main result about Gaussian continuity and boundedness, due originally, more or less in the f”
On the limiting distributions of multivariate depth-based rank sum statistics and related tests (2006, neutral): “5 of [6]), we have, for any ε > 0, that P(Dm(H) > M) ≤ Ke−(2−ε)M(2) for some sufficiently large constant K = K(ε,S(H)).”