On weak* convergence in ¹

By Joseph A. Cima, A. Matheson. 1996

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Citations in the corpus

Double/De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers (2018, methodology): “We use notation from the empirical process theory, see Van Der Vaart and Wellner (1996).”
Monge-Kantorovich Depth, Quantiles, Ranks and Signs (2014, methodology): “The proof is an immediate consequence of the extended continuous mapping theorem, as given in van der Vaart and Wellner [56], Theorem A.1 and Corollary A.1.”
Inference for empirical Wasserstein distances on finite spaces (2016, background): “Van der Vaart and Wellner (1996)) the derivative h 7→ f ′ u(h) is not required to be linear.”
Stratification Trees for Adaptive Randomization in Randomized Controlled Trials (2018, methodology): “In our setting the stratification is random, and so to prove our result we generalize their construction in a way that allows us to re-write the sampling distribution of the estimator as a sequential empirical process (see Van Der Vaart and Wellner, 1996, Section 2.12.1 for a definition).”
Uniformity and the Delta Method (2015, background): “…are used to describe results that guarantee uniform convergence in distribution or probability of random vectors, rather than results that guarantee convergence of empirical processes. van der Vaart and Wellner (1996), p. 379) that guarantees the uniform validity of delta method approximations.”
Minimal dispersion approximately balancing weights: asymptotic properties and practical considerations (2017, methodology): “This assumption is satisfied, for example, by the Hölder class with smoothness parameter s defined on a bounded convex subset of Rd with s/d > 1/2 (van der Vaart & Wellner, 1996; Fan et al., 2016); see also Assumption 4.1.7 in Fan et al. (2016).”
Frequentist coverage and sup-norm convergence rate in Gaussian process regression (2017, methodology): “…implies that the pdf of Z Bn is bounded by some constant independent of ( n, h ) because By applying Borell-Tsirelson-Ibragimov-Sudakov inequality [47, Proposition A.2.1], we obtain that with probability at least 1 − κ/ 2, X (cid:107) F ε ≤ E [ (cid:107) X (cid:107) F ε ] + ε 2 log(4 /κ ) , and…”
Nonparametric estimation in null recurrent time series (2001, methodology): “Since EQ(2)n qn t = t 1+ o 1 we have by an appropriate CLT [Bergstrøm (1981), Theorem 1, page 161] that Qn qn t d → n 0 t for all t. Using a standard argument, the same CLT and the fact that Qn qn has asymptotically independent increments [cf. Billingsley (1968), pages 68 and 69], we find that”
Distribution-on-Distribution Regression via Optimal Transport Maps (2021, methodology): “To this aim, we restate some key theorems from Van Der Vaart and Wellner [19]. where C = sup µ,ν d W ( µ, ν ), and r − 1 n is the rate of estimation of an absolutely continuous measure from n samples.”
Double/de-biased machine learning using regularized Riesz representers (2018, methodology): “We use the notation from the empirical process theory, see Van Der Vaart and Wellner (1996).”