Semiparametric theory and empirical processes in causal inference

@article{Kennedy2016SemiparametricTA,
  title={Semiparametric theory and empirical processes in causal inference},
  author={Edward H. Kennedy},
  journal={arXiv: Statistics Theory},
  year={2016},
  pages={141-167}
}
  • Edward H. Kennedy
  • Published 15 October 2015
  • Mathematics, Economics
  • arXiv: Statistics Theory
In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss estimation and inference for causal effects under semiparametric models, which allow parts of the data-generating process to be unrestricted if they are not of particular interest (i.e., nuisance functions). These models are very useful in causal problems because the… 
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References

SHOWING 1-10 OF 99 REFERENCES
Estimation of semiparametric models
Introduction to Empirical Processes and Semiparametric Inference
Overview.- An Overview of Empirical Processes.- Overview of Semiparametric Inference.- Case Studies I.- Empirical Processes.- to Empirical Processes.- Preliminaries for Empirical Processes.-
Semiparametric Theory for Causal Mediation Analysis: efficiency bounds, multiple robustness, and sensitivity analysis.
TLDR
A general semiparametric framework for obtaining inferences about so-called marginal natural direct and indirect causal effects, while appropriately accounting for a large number of pre-exposure confounding factors for the exposure and the mediator variables is developed.
Estimation of Regression Coefficients When Some Regressors are not Always Observed
Abstract In applied problems it is common to specify a model for the conditional mean of a response given a set of regressors. A subset of the regressors may be missing for some study subjects either
Quadratic semiparametric Von Mises calculus
TLDR
A new method of estimation of parameters in semiparametric and nonparametric models based on U-statistics constructed from quadratic influence functions is discussed, particularly interested in estimating parameters in models with a nuisance parameter of high dimension or low regularity, where the parameter of interest cannot be estimated at n−1/2-rate.
Instruments for Causal Inference: An Epidemiologist's Dream?
TLDR
The definition of an instrumental variable is reviewed, the conditions required to obtain consistent estimates of causal effects are described, and their implications are explored in the context of a recent application of the instrumental variables approach.
Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity
This paper provides a general framework for proving the "square root of" T-consistency and asymptotic normality of a wide variety of semiparametric estimators. The class of estimators considered
Identification of Causal Effects Using Instrumental Variables
TLDR
It is shown that the instrumental variables (IV) estimand can be embedded within the Rubin Causal Model (RCM) and that under some simple and easily interpretable assumptions, the IV estimand is the average causal effect for a subgroup of units, the compliers.
Analysis of sem iparametric regression models for repeated outcomes in the presence of missing data
  • J. Am. Sta t. Assoc.90, 106–121
  • 1995
...
...