Causal Estimation and Predictive Uncertainty: Essays on Robust Statistical Learning

Abstract

This dissertation collects three essays at the intersection of modern statistical learning and applied empirical research. A common thread runs through all three: estimation robustness — the reliability of statistical procedures not under idealized assumptions, but under the conditions actually encountered in practice. The first two essays work within the double machine learning (DML) framework of Chernozhukov et al. (2018); the third addresses predictive uncertainty through conformal prediction.

Chapter 2 — Inference on Multiple Treatment Effects (joint with Cathy Yi-Hsuan Chen, Victor Chernozhukov, and Martin Spindler) extends DML to combinatorial treatment regimes. Marginal attribution is formalized via a regularized tempered policy that confines estimation to empirically supported regions, yielding a probabilistic generalization of the Shapley value. A Method of Simulated Scores estimator resolves computational intractability while preserving consistency and asymptotic normality. The framework is applied to estimate the marginal effects of lifestyle factors on blood pressure using data from the U.S. National Health and Nutrition Examination Survey.

Chapter 3 — Calibration Strategies for Robust Causal Estimation (joint with Sven Klaassen, Jannis Kueck, and Philipp Bach) investigates the effect of post-hoc propensity score calibration on causal estimators within DML. It is established that isotonic calibration preserves the convergence and complexity conditions required by DML theory. A systematic simulation study across four data-generating processes reveals that full-sample calibration applied to cross-fitted propensity scores yields the most stable improvements across calibration methods, sample-splitting schemes, and base learners.

Chapter 4 — Uncertainty Estimation in Insurance Claims Modeling (joint with Michael Merz) develops conformal prediction methods tailored to zero-inflated count data, as encountered in insurance claims portfolios. Standard conformal methods achieve their marginal coverage guarantee by over-covering the majority of policyholders who file no claims, while under-covering the minority of claimants who matter most for actuarial purposes. The essay proposes a two-stage framework combining Mondrian conformal prediction for the claim/no-claim decision with dynamically grouped conformal prediction for positive counts. Simulations and an application to German motor insurance data demonstrate balanced outcome-conditional coverage where standard methods systematically fail. A Burt distance-based clustering diagnostic identifies portfolio segments with elevated prediction uncertainty.