Counterfactual CDFs are pathwise differentiable iff a square-integrable dual bridge exists, with root-n estimation possible exactly when a singular-value summability condition and residual moment hold, enabling uniform doubly robust quantile bands and CVaR inference.
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A neural doubly robust proxy causal learning framework using mean embeddings for treatment bridges provides consistent estimators for causal dose-response functions under unobserved confounding for continuous and structured treatments.
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Regularity, Phase Transitions, and Uniform Inference for Proximal Counterfactual Quantile Processes
Counterfactual CDFs are pathwise differentiable iff a square-integrable dual bridge exists, with root-n estimation possible exactly when a singular-value summability condition and residual moment hold, enabling uniform doubly robust quantile bands and CVaR inference.
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Doubly Robust Proxy Causal Learning with Neural Mean Embeddings
A neural doubly robust proxy causal learning framework using mean embeddings for treatment bridges provides consistent estimators for causal dose-response functions under unobserved confounding for continuous and structured treatments.