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A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
Nuisance Function Tuning and Sample Splitting for Optimal...
[Submitted on 30 Dec 2022 (v1), last revised 5 Sep 2026 (this ve · 2022-12-31 · via stat updates on arXiv.org

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Abstract:Estimators of doubly robust functionals typically rely on estimating two complex nuisance functions, such as the propensity score and conditional outcome mean for the average treatment effect functional. We consider the problem of how to estimate nuisance functions to obtain optimal rates of convergence for a doubly robust nonparametric functional that has witnessed applications across the causal inference and conditional independence testing literature. For several plug-in estimators and a first-order bias-corrected estimator, we illustrate the interplay between different tuning parameter choices for the nuisance function estimators and sample splitting strategies on the optimal rate of estimating the functional of interest. For each of these estimators and each sample splitting strategy, we show the necessity to either undersmooth or oversmooth the nuisance function estimators under low regularity conditions to obtain optimal rates of convergence for the functional of interest. Unlike the existing literature, we show that plug-in and first-order bias-corrected estimators can achieve minimax rates of convergence across all Hölder smoothness classes of the nuisance functions by careful combinations of sample splitting and nuisance function tuning strategies. We complement these results with numerical simulations illustrating the impact of different nuisance function tuning and sample splitting strategies.

Submission history

From: Sean McGrath [view email]
[v1] Fri, 30 Dec 2022 18:17:06 UTC (31 KB)
[v2] Wed, 29 May 2024 19:19:46 UTC (585 KB)
[v3] Tue, 13 Aug 2024 00:24:01 UTC (953 KB)
[v4] Sun, 8 Mar 2026 19:35:56 UTC (1,774 KB)
[v5] Sat, 5 Sep 2026 05:41:55 UTC (2,617 KB)