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Abstract:
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The presence of confounding by high-dimensional variables complicates estimation of the average causal effect of a point exposure. It necessitates the use of variable selection strategies and/or data-adaptive high-dimensional statistical methods, which tend to deliver estimators with large bias and non-standard asymptotic behavior.
In this talk, I will introduce penalised bias-reduced double-robust estimation of the average causal effect, which extends work by Vermeulen and Vansteelandt (JASA 2015), and will show that it delivers estimators of the average causal effect that have a small bias property, even under model misspecification. This means that their bias vanishes faster than the bias in the nuisance parameter estimators when the smoothing parameter (e.g., the parameter of the penalisation term) goes to zero, provided that certain sparsity assumptions hold. We exploit this property to obtain valid (uniform) inference.? Considered simulation studies, including the ones from the prior literature (e.g., Belloni et al., JBES 2012, Farrell, JE 2015), show promising performance relative to the competing proposals.
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