Fast Online Inference On Semiparametric Models

Xiaohong Chen, Elie Tamer and Qingsong Yao
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Xiaohong Chen: Yale University
Elie Tamer: Harvard University
Qingsong Yao: Louisiana State University

No 2548, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper develops a framework for fast online inference on semiparametric models with large sample sizes and possibly many covariates. The computational algorithm itself is the object of statistical study: after a globally consistent warm start in the first phase, the path of averaged online iterates generated in the second phase automatically delivers estimators with optimal convergence rates and valid confidence sets. Both phases require only a single pass over the data stream and are well suited to streaming data or to settings with storage/privacy constraints. For semiparametric monotone index models, the averaged trajectory of the second phase lead to estimators that are automatically orthogonalized and satisfy the laws of the iterated logarithms, and policy functionals are updated along the same trajectory at negligible additional cost. The averaged trajectories satisfy functional central limit theorems, which yield fast online inference via random scaling and bypass the explicit variance estimation that complicates inference for semiparametric models. Applied to a fixed large sample, our online algorithm achieves substantial computational gains over corresponding offline procedures without sacrificing statistical performance. Monte Carlo experiments show adequate behavior. Our methods are applied to 19 million traffic-stop online records from the North Carolina State Patrol (Pierson et al. 2020) and to the international trade data of Helpman et al. (2008) with over 300 regressors. We also compare our estimator to its parametric benchmark in both empirical illustrations.

Pages: 157 pages
Date: 2026-07-27
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