Introduction to Empirical Processes and Semiparametric Inference

By Michael R. Kosorok. 2008

716 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

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Citations in the corpus

Interpretable Distribution Features with Maximum Testing Power (2016, background): “Lemma 7 (properties of VC classes, see page 141, 146-147 in van der Vaart and Wellner (2000) and page 160-161 in Kosorok (2008)) .”
Efficiently Breaking the Curse of Horizon in Off-Policy Evaluation with Double Reinforcement Learning (2019, background): “In particular, we suppose that we are given some class )) be the bracketing integral, i.e. , the integral of its square-root-log bracketing number under the L p ( p ∞ b ) norm (see Kosorok, 2008, p. 17).”
Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes (2019, background): “For a more general and complete presentation, we refer the reader to Bickel et al. (1998); Kosorok (2008); Tsiatis (2006); van der Vaart (1998).”
Threshold quantile autoregressive models (2011, neutral): “Now Theorem 11.4 in Kosorok (2008) yields E∗ sup d̃(θ,θ0) δ |GTA2(θ)| = E∗‖GT ‖F × ‖F‖P,2 ≤ δ2.”
A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing (2013, neutral): “1 in Kosorok [29], that, for any m ∈ {1, .”
Goodness‐of‐fit testing based on a weighted bootstrap: A fast large‐sample alternative to the parametric bootstrap (2012, positive): “This resampling technique, based on the multiplier central limit theorem for empirical processes (see e.g. van der Vaart and Wellner, 2000; Kosorok, 2008), was recently used for assessing the goodness of fit of copula models in Kojadinovic, Yan, and Holmes (2011).”
Inference on breakdown frontiers (2017, methodology): “7 on page 189 of Kosorok (2008), we can apply a continuous mapping theorem to get”
Pivotal estimation via square-root Lasso in nonparametric regression (2011, background): “Generally, if we have a score, which identifies the target parameter but does not have the orthogonality property, we can construct the score that has the required property by projecting the original score onto the orthocomplement of the tangent space for the nuisance parameter; see, for example, [3”
DELTA METHOD IN LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR ESTIMATORS (2011, methodology): “More recently, van der Vaart and Wellner (1996) and Kosorok (2008) provided an excellent summary of the functional delta method in terms of a weak convergence.”
Uniformly Semiparametric Efficient Estimation of Treatment Effects With a Continuous Treatment (2015, background): “, Newey (1984), Murphy and Topel (1985), Newey and McFadden (1994), Chernozhukov and Hong (2002), Hirano and Imbens (2004), and Wei and Carroll (2009).”
Q-LEARNING WITH CENSORED DATA (2012, result): “Similar results for Glivenko–Cantelli classes, Donsker classes and bounded uniform entropy integral (BUEI) classes can be found in van der Vaart and Wellner (1996) and Kosorok (2008).”
Nonparametric inference in generalized functional linear models (2014, neutral): “4 of [21] that for any δ > 0 ∥∥∥∥ sup θ,θ̃∈Fpn ‖θ−θ̃‖2≤δ ‖Hn(θ)−Hn(θ̃)‖ ∥∥∥∥ ψ2”
Uniform post-selection inference for least absolute deviation regression and other Z-estimation problems (2013, background): “4 in [17]), and inference about α0 based on this estimator provides best minimax power against local alternatives (see Theorem 18.”
A note on bootstrap approximations for the empirical copula process (2010, neutral): “Moreover, Cn = Φ(Fn) and C = Φ(C), and consequently the functional delta method [see Kosorok (2008)] yields √ n µ τ (C∗n − Cn) = √ n µ τ (Φ(F ∗n)− Φ(Fn)) P ξ Φ′C(BC) = GC , where the derivative of the map Φ at the point C is given by Φ′C(H)(u1, u2) = H(u1, u2)− ∂1C(u1, u2)H(u1,∞)− ∂2C(u1, u2)H(∞,…”