Online Learning in Semiparametric Econometric Models

2026-03-09

AI Summary

This study addresses the challenge of real-time updating and inference for streaming economic and financial data within traditional semiparametric econometric models. To this end, we propose an online learning framework tailored to semiparametric monotonic index models. Our approach employs a two-stage paradigm that integrates globally stable online initialization, an orthogonalized score-based updating mechanism, and an online sieve method, enabling joint estimation of finite-dimensional parameters and the unknown monotonic link function using only the most recent data batch. The estimator achieves optimal convergence rates and innovatively supports real-time construction of confidence regions and policy effect analysis. Extensive simulations and empirical experiments demonstrate that our method substantially outperforms full-sample alternatives while offering markedly improved computational efficiency.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• online learning
• semiparametric models
• streaming data
• monotone index models
• real-time inference

Innovation

• online learning
• semiparametric models
• monotone index model
• online sieve method
• orthogonalized score