publications

2025

1. AoS

   Strong approximations for empirical processes indexed by Lipschitz functions

   Matias D Cattaneo, and Ruiqi (Rae) Yu

   Annals of Statistics, forthcoming, 2025

   Abs Bib HTML PDF

   This paper presents new uniform Gaussian strong approximations for empirical processes indexed by classes of functions based on \(d\)-variate random vectors (\(d \geq1 \)). First, a uniform Gaussian strong approximation is established for general empirical processes indexed by possibly Lipschitz functions, improving on previous results in the literature. In the setting considered by [Rio (1994)], and if the function class is Lipschitzian, our result improves the approximation rate \(n^{-1/(2d)}\)to \(n^{-1/\max\{d,2\}}\), up to a \(polylog(n)\)term, where \(n\)denotes the sample size. Remarkably, we establish a valid uniform Gaussian strong approximation at the rate \(n^{-1/2}\log n\)for \(d=2\), which was previously known to be valid only for univariate (\(d=1\)) empirical processes via the celebrated Hungarian construction [Komlós, Major, Tusnády (1975)]. Second, a uniform Gaussian strong approximation is established for multiplicative separable empirical processes indexed by possibly Lipschitz functions, which addresses some outstanding problems in the literature [Chernozhukov, Chetverikov, Kato (2014)]. Finally, two other uniform Gaussian strong approximation results are presented when the function class is a sequence of Haar basis based on quasi-uniform partitions. Applications to nonparametric density and regression estimation are discussed.

   @article{cattaneo2024strong,
     title = {Strong approximations for empirical processes indexed by Lipschitz functions},
     author = {Cattaneo, Matias D and Yu, Ruiqi (Rae)},
     journal = {Annals of Statistics, forthcoming},
     year = {2025},
     url = {https://arxiv.org/abs/2406.04191},
   }

2. arXiv

   Robust Inference for the Direct Average Treatment Effect with Treatment Assignment Interference

   Matias D Cattaneo, Yihan He, and Ruiqi (Rae) Yu

   arXiv preprint arXiv:2502.13238, 2025

   Abs Bib HTML PDF

   Uncertainty quantification in causal inference settings with random network interference is a challenging open problem. We study the large sample distributional properties of the classical difference-in-means Hajek treatment effect estimator, and propose a robust inference procedure for the (conditional) direct average treatment effect, allowing for cross-unit interference in both the outcome and treatment equations. Leveraging ideas from statistical physics, we introduce a novel Ising model capturing interference in the treatment assignment, and then obtain three main results. First, we establish a Berry-Esseen distributional approximation pointwise in the degree of interference generated by the Ising model. Our distributional approximation recovers known results in the literature under no-interference in treatment assignment, and also highlights a fundamental fragility of inference procedures developed using such a pointwise approximation. Second, we establish a uniform distributional approximation for the Hajek estimator, and develop robust inference procedures that remain valid regardless of the unknown degree of interference in the Ising model. Third, we propose a novel resampling method for implementation of robust inference procedure. A key technical innovation underlying our work is a new \textitDe-Finetti Machine that facilitates conditional i.i.d. Gaussianization, a technique that may be of independent interest in other settings.

   @article{cattaneo2025robust,
     title = {Robust Inference for the Direct Average Treatment Effect with Treatment Assignment Interference},
     author = {Cattaneo, Matias D and He, Yihan and Yu, Ruiqi (Rae)},
     journal = {arXiv preprint arXiv:2502.13238},
     year = {2025},
     url = {https://arxiv.org/abs/2502.13238},
   }