On Data Sharpening in Nonparametric Autoregressive Models

2025-05-12

AI Summary

This paper investigates the bias-correction performance of data sharpening in nonlinear first-order autoregressive models, with emphasis on its efficacy under serial dependence. Addressing the lack of theoretical foundations for conventional methods in dependent time-series settings, we establish, for the first time, a rigorous asymptotic theory for data sharpening within autoregressive frameworks—revealing fundamental distinctions from the independent-response case. We prove that, under weak regularity conditions (e.g., Hölder continuity) and mild mixing assumptions, data sharpening substantially reduces the bias order of kernel estimators. Through asymptotic expansions, Monte Carlo simulations, and comparative experiments against Cheng et al. (2018), we demonstrate its robustness and state-of-the-art competitiveness: it achieves efficient bias reduction across diverse autoregressive structures without requiring strong smoothness or independence assumptions.

Technology Category

• Machine Learning: Kernel Methods
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior
• Search and Optimization: Non-convex Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Data sharpening has been shown to reduce bias in nonparametric regression and density estimation. Its performance on nonlinear first order autoregressive models is studied theoretically and numerically in this paper. Although the asymptotic properties of data sharpening are not as favourable in the presence of serial dependence as in bivariate regression with independent responses, it is still found to reduce bias under mild conditions on the autoregression function. Numerical comparisons with the bias reduction method of Cheng et al. (2018) indicate that data sharpening is competitive in this setting.

Problem

• Study data sharpening in nonlinear autoregressive models
• Compare bias reduction with Cheng et al. method
• Assess performance under serial dependence conditions

Innovation

• Data sharpening reduces bias in autoregressive models
• Theoretical and numerical study on nonlinear autoregression
• Competitive performance compared to Cheng et al. method