Asymptotic statistics

By François Bachoc. 2018

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Citations in the corpus

Machine Learning Methods That Economists Should Know About (2019, neutral): “2 Support Vector Machines and Kernels Support Vector Machines (SVMs, Vapnik [1998], Scholkopf and Smola [2001]) are another flexible set of methods for classification analyses.”
Protection Against Reconstruction and Its Applications in Private Federated Learning (2018, positive): “Indeed, we have (for error i an error term in the Taylor expansion of (cid:96) ), which—when carried out rigorously—implies The inﬂuence function ψ [63] of the parameter θ measures the eﬀect that changing a single observation X i has on the resulting estimator (cid:98) θ n .”
Estimation and Inference of Heterogeneous Treatment Effects using Random Forests (2015, positive): “As with all projections [Van der Vaart, 2000], E ˆ µ ( x ) − ˚ˆ µ ( x ) 2 = Var ˆ µ ( x ) − ˚ˆ µ ( x ) .”
Verified Uncertainty Calibration (2019, positive): “23 of [43], on the asymptotic parameter convergence of M-estimators, we have as n→∞: √ n(θ̂ − θ)→D N(0,Σ) Then for each 1 ≤ i ≤ d, we have: √ n(θ̂i − θ∗ i )→D N(0, σ(2) i ) We will show that there exists ci such that for each i and for all n, with probability at least 1− δ d : |θ̂i − θ∗ i | ≤ ci n”
Efficiently Breaking the Curse of Horizon in Off-Policy Evaluation with Double Reinforcement Learning (2019, positive): “…seminal work of H´ajek (1970, 1972) shows that the CR bound (times n ) is also a lower bound on the asymptotic MSE of any regular estimator, or of any estimator almost everywhere, or of any estimator in some vanishing neighborhood of θ 0 (van der Vaart, 1998, Theorems 8.8, 8.9, 8.11, respectively).”
Intrinsically Efficient, Stable, and Bounded Off-Policy Evaluation for Reinforcement Learning (2019, neutral): “7 in [28], the statement holds from (a1), (a3) and the above uniform convergence condition.”
An Explanation of In-context Learning as Implicit Bayesian Inference (2021, critical): “The canonical Bayesian asymptotic tool is the Bernstein-von Mises theorem (van der Vaart,1998;Kleijn&vanderVaart,2012;Gunst&Shcherbakova,2008), whichasserts(underregularity conditions) that the posterior distribution of a latent variable concentrates on the maximum likelihood estimate.”
Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes (2019, methodology): “Without sample splitting, we have to assume a Donsker condition for the class of estimators in order to control a stochastic equicontinutiy term (see, e.g. , van der Vaart, 1998, Lemma 19.24).”
Sliced Score Matching: A Scalable Approach to Density and Score Estimation (2019, neutral): “These are standard assumptions used for proving the consistency of MLE (van der Vaart, 1998).”
Gaussian Process Behaviour in Wide Deep Neural Networks (2018, background): “We can therefore invoke a general result on convergence of sequences that says if a sequence of random variables X i converges to X ∗ and | X i − Y i | converges in probability to zero, then Y i converges in distribution to X ∗ (Vaart, 1998).”
The Right Complexity Measure in Locally Private Estimation: It is not the Fisher Information (2018, neutral): “Indeed, Le Cam’s theory of quadratic mean diﬀerentiability, contiguity, local asymptotic normality, and local alternatives for testing all reposes on closeness in Hellinger distance [34, 35, 42, 50], which justiﬁes the use of Fisher Information in classical statistical problems.”
Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm (2005, unknown): “All these methods require considerable A u t h o r ' s p e r s o n a l”
Statistical Mechanics of Optimal Convex Inference in High Dimensions (2016, unknown): “We give an intuitive summary of our results in the discussion section.”
Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions (2018, unknown): “We then see from standard arguments from asymptotic semiparametric statistics [51] that the asymptotic variance occuring in Theorems 3 and 4 is optimal in an information-theoretic sense.”