High-dimensional Inference for Dynamic Treatment Effects
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This paper proposes a confidence interval construction for heterogeneous treatment effects in the context of multi-stage experiments with N samples and high-dimensional, d, confounders. Our focus is on the case of d≫ N, but the results obtained also apply to low-dimensional cases. We showcase that the bias of regularized estimation, unavoidable in high-dimensional covariate spaces, is mitigated with a simple double-robust score. In this way, no additional bias removal is necessary, and we obtain root-N inference results while allowing multi-stage interdependency of the treatments and covariates. Memoryless property is also not assumed; treatment can possibly depend on all previous treatment assignments and all previous multi-stage confounders. Our results rely on certain sparsity assumptions of the underlying dependencies. We discover new product rate conditions necessary for robust inference with dynamic treatments.
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