arXiv subjects

Gabriel Saco

Publications and source records attributed to Gabriel Saco.

2 recordsLinked to original sources

arXiv2026

Fixed-Horizon Self-Normalized Inference for Adaptive Experiments via Martingale AIPW/DML with Logged Propensities

Adaptive randomized experiments update treatment probabilities as data accrue, but still require an end-of-study interval for the average treatment effect (ATE) at a prespecified horizon. Under adaptive assignment, propensities can keep changing, so the predictable quadratic variation of AIPW/DML score increments may remain random. When no deterministic variance limit exists, Wald statistics normalized by a single long-run variance target can be conditionally miscalibrated given the realized variance regime. We assume no interference, sequential randomization, i.i.d. arrivals, and executed overlap on a prespecified scored set, and we require two auditable pipeline conditions: the platform logs the executed randomization probability for each unit, and the nuisance regressions used to score unit $t$ are constructed predictably from past data only. These conditions make the centered AIPW/DML scores an exact martingale difference sequence. Using self-normalized martingale limit theory, we show that the Studentized statistic, with variance estimated by realized quadratic variation, is asymptotically N(0,1) at the prespecified horizon, even without variance stabilization. Simulations validate the theory and highlight when standard fixed-variance Wald reporting fails.

stat.ME↗

arXiv2025

Ill-Conditioned Orthogonal Scores in Double Machine Learning

Double Machine Learning is often justified by nuisance-rate conditions, yet finite-sample reliability also depends on the conditioning of the orthogonal-score Jacobian. This conditioning is typically assumed rather than tracked. When residualized treatment variance is small, the Jacobian is ill-conditioned and small systematic nuisance errors can be amplified, so nominal confidence intervals may look precise yet systematically under-cover. Our main result is an exact identity for the cross-fitted PLR-DML estimator, with no Taylor approximation. From this identity, we derive a stochastic-order bound that separates oracle noise from a conditioning-amplified nuisance remainder and yields a sufficiency condition for root-n-inference. We further connect the amplification factor to semiparametric efficiency geometry via the Riesz representer and use a triangular-array framework to characterize regimes as residual treatment variation weakens. These results motivate an out-of-fold diagnostic that summarizes the implied amplification scale. We do not propose universal thresholds. Instead, we recommend reporting the diagnostic alongside cross-learner sensitivity summaries as a fragility assessment, illustrated in simulation and an empirical example.

stat.ME↗