Semiparametric theory and empirical processes in causal inference

By Edward H. Kennedy. 2015

205 citations recorded by the source corpus.

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 outcome process is often complex and difficult to model, and there may only be information available about the treatment process (at best). Semiparametric theory gives a framework for benchmarking efficiency and constructing estimators in such settings. In the second part of the paper we discuss empirical process theory, which provides powerful tools for understanding the asymptotic behavior of semiparametric estimators that depend on flexible nonparametric estimators of nuisance functions. These tools are crucial for incorporating machine learning and other modern methods into causal inference analyses. We conclude by examining related extensions and future directions for work in semiparametric causal inference.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0a6a9e5c3ea9d0aaf7017dc31beb973dbf964592

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Citations in the corpus

Time-uniform central limit theory and asymptotic confidence sequences (2021, background): “Examples include (a) nonparametric estimation of means, such as population proportions, (b) maximum likelihood and other M-estimation problems [58], and (c) modern semiparametric causal inference methodology involving (augmented) inverse propensity score weighting [44, 56, 24, 8].”
Minimal dispersion approximately balancing weights: asymptotic properties and practical considerations (2017, background): “tion error of the propensity score and the outcome functions, respectively. This assumption relates to the product structure of error bounding in doubly robust estimation; see, e.g., Equation (41) of Kennedy (2016). Theorem 3. Suppose that the conditions in assumptions 1 and 2 hold. Then n1/2(Yˆ w⁄ ”
Adapting Text Embeddings for Causal Inference (2019, background): “ ˜(f(t i, yi,ˆi)g;˜) p ! . Remark 4.3. The requirement that the estimator ˆ behaves asymptotically as a sample mean is not an important restriction; most commonly used estimators have this property [Ken16]. The third condition is a technical requirement on the estimator. In the cases we consider, it”
The Generalized Oaxaca-Blinder Estimator (2020, background): “See Rothe (2018), Kennedy (2016), and the discussion in Chernozhukov et al. (2018). For stable sequences {μ̂n}n≥1, these bounds will be satisfied as long as μ̂n is “simple” enough to not overfit the data. Examples include smooth parametric models of fixed dimension, classifiers in a VC class, regres”
Adapting Neural Networks for the Estimation of Treatment Effects (2019, background): “Such estimators are studied in the semi-parametric estimation literature; see Kennedy [ Ken16 ] for a readable introduction.”
Counterfactual risk assessments, evaluation, and fairness (2019, methodology): “In a non-parametric setting, DR methods have faster rates of convergence than propensity-score methods [23].”
Using Text Embeddings for Causal Inference (2019, background): “The requirement that the estimator ˆ ψ behaves asymptotically as a sample mean is not an important restriction; most commonly used estimators have this property [ Ken16 ] .”
Semiparametric doubly robust targeted double machine learning: a review (2022, background): “…describe this approach for two primary reasons: (i) as the more classical approach, there are already widely available references [Andrews, 1994, Kennedy, 2016, Kosorok, 2008, van der Vaart, 2000, 2002, van der Vaart and Wellner, 1996], (ii) the second way to control the term T 1 , using…”