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In this review we cover the basics of efficient nonparametric parameter estimation (also called functional estimation), with a focus on parameters that arise in causal inference problems.
Sparsity double robust inference of average treatment effects
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R. von Mises · 1947
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Efficient nonparametric testing and estimation
C. Stein · 1956
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R. Z. Hasminskii and I. A. Ibragimov · 1978
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Contributions to a general asymptotic statistical theory , volume 13
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A new approach to causal inference in mortality studies with a sustained exposure period - application to control of the healthy worker survivor effect
J. M. Robins · 1986
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On asymptotically efficient estimation in semiparametric models
A. Schick · 1986
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Estimating integrated squared density derivatives: sharp best order of convergence estimates
P. J. Bickel and Y. Ritov · 1988
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Efficient and Adaptive Estimation for Semiparametric Models
P. J. Bickel, C. A. Klaassen, Y. Ritov, and J. A. Wellner · 1993
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Empirical process methods in econometrics
D. W. Andrews · 1994
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The asymptotic variance of semiparametric estimators
W. K. Newey · 1994
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Estimation of integral functionals of a density
L. Birgé and P. Massart · 1995
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Weak Convergence and Empirical Processes
A. W. van der Vaart and J. A. Wellner · 1996
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Asymptotic Statistics
A. W. van der Vaart · 2000
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Statistical Inference
G. Casella and R. L. Berger · 2001
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Comments on: Inference for semiparametric models: Some questions and an answer
J. M. Robins and A. Rotnitzky · 2001
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A Distribution-Free Theory of Nonparametric Regression
L. Györfi, M. Kohler, A. Krzykaz, and H. Walk · 2002
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Semiparametric statistics
A. W. van der Vaart · 2002
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Optimal dynamic treatment regimes
S. A. Murphy · 2003
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Unified Methods for Censored Longitudinal Data and Causality
M. J. van der Laan and J. M. Robins · 2003
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Extending marginal structural models through local, penalized, and additive learning
D. B. Rubin and M. J. van der Laan · 2006
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Semiparametric Theory and Missing Data
A. A. Tsiatis · 2006
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Targeted maximum likelihood learning
M. J. van der Laan and D. B. Rubin · 2006
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Introduction to empirical processes and semiparametric inference
M. R. Kosorok · 2008
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Higher order influence functions and minimax estimation of nonlinear functionals
J. M. Robins, L. Li, E. J. Tchetgen Tchetgen, and A. W. van der Vaart · 2008
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Causality: Models, Reasoning, and Inference
J. Pearl · 2009
Cited alongside, same era.
Estimation of the causal effects of time-varying exposures
J. M. Robins and M. A. Hernán · 2009
Cited alongside, same era.
Quadratic semiparametric von mises calculus
J. M. Robins, L. Li, E. J. Tchetgen Tchetgen, and A. W. van der Vaart · 2009
Cited alongside, same era.
Introduction to Nonparametric Estimation
A. B. Tsybakov · 2009
Cited alongside, same era.
Identification, inference and sensitivity analysis for causal mediation effects
K. Imai, L. Keele, and T. Yamamoto · 2010
Cited alongside, same era.
Semiparametric theory and empirical processes in causal inference
E. H. Kennedy · 2016
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Statistical inference for the mean outcome under a possibly non-unique optimal treatment strategy
A. R. Luedtke and M. J. van der Laan · 2016
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Nonparametric methods for doubly robust estimation of continuous treatment effects
E. H. Kennedy, Z. Ma, M. D. McHugh, and D. S. Small · 2017
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Causal inference for social network data
E. L. Ogburn, O. Sofrygin, I. Diaz, and M. J. Van Der Laan · 2017
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Minimax estimation of a functional on a structured high dimensional model
J. M. Robins, L. Li, R. Mukherjee, E. J. Tchetgen Tchetgen, and A. W. van der Vaart · 2017
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Asymptotic theory for cross-validated targeted maximum likelihood estimation
W. Zheng and M. J. van der Laan · 2010
Cited alongside, same era.
Higher order inference on a treatment effect under low regularity conditions
L. Li, E. T. Tchetgen, A. van der Vaart, and J. M. Robins · 2011
Cited alongside, same era.
Targeted Learning: Causal Inference for Observational and Experimental Data
M. J. van der Laan and S. Rose · 2011
Cited alongside, same era.
Population intervention causal effects based on stochastic interventions
I. Díaz and M. J. van der Laan · 2012
Cited alongside, same era.
Impossibility results for nondifferentiable functionals
K. Hirano and J. R. Porter · 2012
Cited alongside, same era.
Semiparametric theory for causal mediation analysis: efficiency bounds, multiple robustness, and sensitivity analysis
E. J. Tchetgen Tchetgen and I. Shpitser · 2012
Cited alongside, same era.
Estimation and inference about conditional average treatment effect and other structural functions
V. Semenova and V. Chernozhukov · 2017
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Double/debiased machine learning for treatment and structural parameters
V. Chernozhukov, D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, W. Newey, and J. M. Robins · 2018
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Semiparametric theory
E. H. Kennedy · 2018
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Causal effects based on distributional distances
K. Kim, J. Kim, and E. H. Kennedy · 2018
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Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables
L. Wang and E. Tchetgen Tchetgen · 2018
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Orthogonal statistical learning
D. J. Foster and V. Syrgkanis · 2019
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Nonparametric causal effects based on incremental propensity score interventions
E. H. Kennedy · 2019
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Characterization of parameters with a mixed bias property
A. Rotnitzky, E. Smucler, and J. M. Robins · 2019
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Machine learning in the estimation of causal effects: targeted minimum loss-based estimation and double/debiased machine learning
I. Díaz · 2020
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Optimal doubly robust estimation of heterogeneous causal effects
E. H. Kennedy · 2020
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Sharp instruments for classifying compliers and generalizing causal effects
E. H. Kennedy, S. Balakrishnan, and M. G’Sell · 2020
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An introduction to proximal causal learning
E. J. Tchetgen Tchetgen, A. Ying, Y. Cui, X. Shi, and W. Miao · 2020
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A unified study of nonparametric inference for monotone functions
T. Westling and M. Carone · 2020
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Deep neural networks for estimation and inference
M. H. Farrell, T. Liang, and S. Misra · 2021
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Visually communicating and teaching intuition for influence functions
A. Fisher and E. H. Kennedy · 2021
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Semiparametric counterfactual density estimation
E. H. Kennedy, S. Balakrishnan, and L. Wasserman · 2021
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Quasi-oracle estimation of heterogeneous treatment effects
X. Nie and S. Wager · 2021
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Demystifying statistical learning based on efficient influence functions
O. Hines, O. Dukes, K. Diaz-Ordaz, and S. Vansteelandt · 2022
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The influence function of semiparametric estimators
H. Ichimura and W. K. Newey · 2022
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Minimax rates for heterogeneous causal effect estimation
E. H. Kennedy, S. Balakrishnan, and L. Wasserman · 2022
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