Optimal One-Pass Nonparametric Estimation Under Memory Constraint

• 成果类型: Article
• 署名作者: Quan, Mingxue; Lin, Zhenhua
• 署名单位: Renmin University of China; National University of Singapore
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2115374
• 发表日期: 2024
• 页码: 285-296
• 关键词: convergence; regression; dependence; rates

摘要

For nonparametric regression in the streaming setting, where data constantly flow in and require real-time analysis, a main challenge is that data are cleared from the computer system once processed due to limited computer memory and storage. We tackle the challenge by proposing a novel one-pass estimator based on penalized orthogonal basis expansions and developing a general framework to study the interplay between statistical efficiency and memory consumption of estimators. We show that, the proposed estimator is statistically optimal under memory constraint, and has asymptotically minimal memory footprints among all one-pass estimators of the same estimation quality. Numerical studies demonstrate that the proposed one-pass estimator is nearly as efficient as its nonstreaming counterpart that has access to all historical data.