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Online Learning in Semiparametric Econometric Models

Xiaohong Chen, Elie Tamer, Qingsong Yao

arXiv 9 Mar 2026 · Econometrics

arXiv:2603.08614 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Data in modern economic and financial applications often arrive as a stream, requiring models and inference to be updated in real time -- yet most semiparametric methods remain batch-based and computationally impractical in large-scale streaming settings. We develop an online learning framework for semiparametric monotone index models with an unknown monotone link function. Our approach uses a two-phase learning paradigm. In a warm-start phase, we introduce a new online algorithm for the finite-dimensional parameter that is globally stable, yielding consistent estimation from arbitrary initialization. In a subsequent rate-optimal phase, we update the finite-dimensional parameter using an orthogonalized score while learning the unknown link via an online sieve method; this phase achieves optimal convergence rates for both components. The procedure processes only the most recent data batch, making it suitable when data cannot be stored (e.g., memory, privacy, or security constraints), and its resulting parameter trajectories enable online inference such as confidence regions--on parameters including policy-effect analysis with negligible additional computation. Monte Carlo experiments on both simulated and real data show adequate performance especially relative to full sample methods.

Citation extraction

45
references
81
in-text mentions
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distinct cited
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Lee, Sokbae and Liao, Yuan and Seo, Myung Hwan and Shin, Youngki (2022) Fast and robust online inference with stochastic gradient descent via random scaling1.00053100%
2Chen, Xiaohong and Christensen, Timothy M (2015) Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions self0.9507386%
3Khan, Shakeeb and Tamer, Elie and Yao, Qingsong (2024) Inference on High Dimensional Selective Labeling Models self0.92843100%
4Khan, Shakeeb and Lan, Xiaoying and Tamer, Eile and Yao, Qingsong (2024) Estimating High Dimensional Monotone Index Models By Iterative Convex Optimization self0.92843100%
5Han, Aaron K (1987) Non-parametric analysis of a generalized regression model: the maximum rank correlation estimator0.81142100%
6Chen, Xiaohong and Lee, Sokbae and Liao, Yuan and Seo, Myung Hwan an… (2023) SGMM: Stochastic approximation to generalized method of moments self0.73732100%
7Chen, Xiaohong and Kim, Min Seong and Lee, Sokbae and Seo, Myung Hwa… (2025) SLIM: Stochastic Learning and Inference in Overidentified Models self0.73732100%
8Belloni, Alexandre and Chernozhukov, Victor and Chetverikov, Denis a… (2015) Some new asymptotic theory for least squares series: Pointwise and uniform results0.64422100%
9Chen, Xiaohong (2007) Large sample sieve estimation of semi-nonparametric models self0.64422100%
10Huang, Yinxiao and Chen, Xiaohong and Wu, Wei Biao (2013) Recursive nonparametric estimation for time series self0.64422100%

Showing the top 10 of 45 scored citations.