ON DIFFERENTIABLE FUNCTIONALS

By Aad Van Der Vbart. 1988

How researchers see this paper

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

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).”
Double/debiased machine learning for treatment and structural parameters (2017, unknown): “1, if the score ψ is efficient for estimating θ0 at a given P ∈ P ⊂ PN , in the semi-parametric sense as defined in van der Vaart (1998), then the large sample variance σ(2) 0 of θ̃0 reaches the semi-parametric efficiency bound at this P relative to the model P.”
The influence function of semiparametric estimators (2015, background): “5 of Van der Vaart (1998) it follows that for any tn = O(1/ √ n) a vector of n observations (z1, .”
Higher Order Tangent Spaces and Influence Functions (2014, background): “Interest is in the situation of a semiparametric or nonparametric model, where H is infinite-dimensional and the dependence η 7→ pη is assumed smooth (as in [16]).”
Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals (2009, unknown): “(i) E [( dm(X,α0) dθ′ )′ Σ0(X) −1 ( dm(X,α0) dθ′ )] is finite, E[Dw(X) ′[Σ0(X)]−1Dw(X)] is fi- nite for any w = (w1, ..., wdθ ) with wj ∈ W0; (ii) for every fixed h ∈ H, p(y, x, θ, ξ) ≡ q0(y, x, θ, h0 + ξ(h− h0)) is smooth in the sense of Van der Vaart (1991).16 Theorem 4.1.”
Double machine learning for treatment and causal parameters (2016, unknown): “See, for example, the important work by [14], [50], [40], [54], [2], [41], [49], [38], [15], [19], [53], and [1].”
Higher order influence functions and minimax estimation of nonlinear functionals (2008, methodology): “Our theory extends the first order semiparametric theory of Bickel et al. (1993) and van der Vaart (1991) by incorporating the theory of higher order scores and Bhattacharrya bases considered by Pfanzagl (1990), Small and McLeish (1994) and Lindsay and Waterman (1996).”
Dynamic treatment regimes: technical challenges and applications (2014, background): “Recall that it is not possible in general to construct a uniformly convergent estimator of the limiting distribution of √ n(β̂1−β∗1) (Van der Vaart, 1991; Hirano and Porter, 2009).”
Learning L2 Continuous Regression Functionals via Regularized Riesz Representers (2018, methodology): “The differences between these methods seem analogous to the difference between nonparametric estimation and root-n consistent functional estimation in the semiparametric literature (see Bickel, Klassen, Ritov, and Wellner, 1993 and Van der Vaart, 1991).”
Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators☆ (2013, background): “The distinctive feature separating the cases is mean-square continuity of the functional θ(·) and its Riesz representation (see, e.g., van der Vaart, 1991).”
MINIMAX ESTIMATION OF A FUNCTIONAL ON A STRUCTURED (2016, background): “, [2, 19, 31, 35]), influence functions are described through inner products with score functions.”
Double/de-biased machine learning using regularized Riesz representers (2018, methodology): “…with low-dimensional X , which focused inference on ideal θ ∗ 0 using traditional smoothing methods for estimating nuisance parameters γ 0 and α 0 [van der Vaart (1991); Newey (1994); Bickel et al. (1998); Robins and Rotnitzky (1995); van der Vaart (1998)], that do not apply to the current…”
Marginal Structural Models versus Structural nested Models as Tools for Causal inference (2000, methodology): “Thus, it is of interest to rederive the efficient score using the Hilbert space results of van der Vaart (1991) and of Robins et al. (1994) for missing data models under CAR.”
Q-Learning: Theory and Applications (2020, background): “Thus, (cid:16) (cid:16) β is the target the regression problem which defines the second step of Q-learning d e d by .”
Program evaluation and causal inference with high-dimensional data (2013, methodology): “…and asymptotically normal estimates for low-dimensional components within traditional semiparametric frameworks as in the important work by Bickel (1982), Robinson (1988), Newey (1990), van der Vaart (1991), Andrews (1994b), Newey (1994), Ai and Chen (2003, 2012), and Chen et al. (2003).”