Valid causal inference: model selection & unobserved confounding

Speaker: Niloofar Moosavi, Department of Statistics, Umeå University

During the last years, a great extent of work has been done on constructing confidence intervals for average causal effect parameters that are uniformly valid over a set of data generating processes even when high-dimensional nuisance models are estimated by post-model-selection or machine learning estimators. These developments assume that all the confounders are observed to ensure point identification. We contribute by showing that valid inference can be obtained in the presence of unobserved confounders and high-dimensional nuisance models. We thus propose uncertainty intervals, which allow for nonzero confounding bias. The later bias is specified and estimated and is function of the amount of unobserved confounding allowed for. We show that valid inference can ignore the finite sample bias and randomness in the estimated value of confounding bias by assuming that the amount of unobserved confounding is small relative to the sample size; the latter is formalized in terms of convergence rates. An interpretation is that more confounders are collected as the sample size grows. Simulation results are presented to illustrate finite sample properties and explore a double selection procedure and a correction of the residual variance estimator, which improve the performance even for larger correlations.

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