Weak convergence and empirical processes

2019

Citations in the corpus

• Generalized random forests (2016, methodology): “The idea of local maximum likelihood (and local generalized method of moments) estimation has a long history, including Fan, Farmen and Gijbels (1998), Newey (1994a), Staniswalis (1989), Stone (1977), Tibshirani and Hastie (1987) and Lewbel (2007).”
• Risk minimization by median-of-means tournaments (2016, background): “…tradeoff is of utmost importance in statistical learning theory, and has been investigated extensively in numerous manuscripts since the early days of the area in the late 1960’s (see, for example, the books [42, 13, 41, 2, 39, 28, 22, 38, 10] for a sample of the work devoted to this question).”
• Multivariate goodness-of-fit tests based on Wasserstein distance (2020, result): “The result is thus a law of large numbers for the empirical distribution in Wasserstein distance uniformly in the underlying distribution akin to Chung’s uniform law of large numbers (van der Vaart and Wellner, 1996, Proposition A.5.1).”
• Nearly optimal central limit theorem and bootstrap approximations in high dimensions (2020, unknown): “2 and discussion on page 95 of [40], and so (log n)(M log d)2 nσ2 ∗,W ≲ B 2 n(log d) 2(log n) log(dn) nσ2 ∗,W ≲ Bn(log d) 3/2 log n √ nσ2 ∗,W (7.”
• Plugin estimation of smooth optimal transport maps (2021, methodology): “The set of Lipschitz functions with a uniform Lipschitz constant forms a GlivenkoCantelli class (van der Vaart and Wellner (1996), Theorem 2.7.1), thus the first term on the righthand side of the above display vanishes in probability.”
• Causal inference with confounders missing not at random (2017, background): “Both spline kernels and Gaussian kernels satisfy Assumption S2 (van der Vaart and Wellner, 1996).”
• A Note on Conditional Versus Joint Unconditional Weak Convergence in Bootstrap Consistency Results (2017, methodology): “Note that the results are stated in terms of nets which generalize sequences (see, e.g., van der Vaart and Wellner, 2000, Section 1.1) in order to account for the net convergences in Assertions (d) and (f) of the two preceding lemmas.”
• Contamination Bias in Linear Regressions (2021, unknown): “To that end, we use the notion of semiparametric efficiency based on the convolution theorem of van der Vaart and Wellner (1989, Theorem 2.1) (see also van der Vaart & Wellner, 1996, Chapter 3.11).”
• Convergence rates of least squares regression estimators with heavy-tailed errors (2017, background): “We make this choice in view of a negative result of Alexander [1], stating that there is no universal moment condition on ξi’s for a multiplier CLT to hold when ξi ’s need not be independent from Xi’s, while a L2,1 moment condition is known to be universal in the independent case [23, 37, 66].”
• Inference on Directionally Differentiable Functions (2014, methodology): “Furthermore, Markov’s inequality, Lemma 1.2.7 in van der Vaart and Wellner (1996), and result (A.40) yield: lim sup n→∞ P (P (G∗n /∈ K δ0 0 |{Xi} n i=1) > ) ≤ lim sup n→∞ P (G∗n /∈ K δ0 0 ) η .”
• Cross-Validation With Confidence (2017, background): “See [32] and [30] for further discussion on the Orlicz norm.”