Online learning and modeling has attracted considerable interest due to increasingly available data in streaming manner. Nonparametric models, although flexible, have seen limited use in online settings due to their data-driven nature and high computational demands. We introduce an innovative online method for dynamically updating local polynomial regression estimates. Our approach decomposes kernel-type estimates into two sufficient statistics and approximates future optimal bandwidths with a dynamic candidate sequence. This idea extends to general nonlinear optimization problems, where we propose an online smoothing backfitting algorithm for generalized additive models (GAM). We establish asymptotic normality and efficiency lower bounds for online estimation, shedding light on the trade-off between accuracy and computational cost driven by the bandwidth sequence length. For GAM, We also investigate statistical and algorithmic convergence and provide a framework for balancing estimation and computation performance. Our proposed online estimation is also applicable to complex structural data such as functional data. Simulations and real data examples are provided to support the usefulness of the proposed method.

About the Guest:

Yao Fang, Professor of Peking University, selected for the National High-level Talent Program, Director of the Statistical Science Center of Peking University, director of the Department of Probability and Statistics. Fellow and Council Member of the International Society for Mathematical Statistics (IMS), Fellow of the American Statistical Association (ASA). He received his bachelor's degree in statistics from the University of Science and Technology of China in 2000, and his doctorate degree in statistics from the University of California, Davis in 2003. He worked as a professor in the Department of Statistical Sciences at the University of Toronto. He has served as editor-in-chief or editorial board member of nine key international journals of Statistics, including editor-in-chief of the Canadian Journal of Statistics and editorial board member of top journals such as the Journal of the American Statistical Association and Annals of Statistics.