计算与应用讨论班

报告题目：Wavelet Methods in Functional Data Analysis: Adaptation in Sparsity, Spatiality and Smoothness

报  告  人：程昆（北京交通大学）

时        间：2025年11月7日（星期五），下午15:00

地        点：海纳苑2幢205

摘        要：Motivated by a large number of applications, there is a great interest in models for observation entities in the form of a sequence of measurements recorded intermittently at several discrete points in time. Functional data analysis (FDA) considers such data as being values on the trajectories of a stochastic process, recorded with some error, at discrete random times. In this talk, we introduce data-driven wavelet methods for FDA, focusing on adaptive estimation and prediction. First, we propose wavelet-based estimators that are easy to implement and adaptively capture local and global features of the underlying functions, regardless of sampling schemes. Estimated convergence rates are established, and in particular, the results reveal a phase transition phenomenon related to the number of observations on each curve. Besides, we integrate an adaptive transformation method into functional linear prediction model and derive its convergence rate. The new proposal is superior to existed methods in mis-specified cases. Simulation studies and real data examples are provided to offer empirical support for the theoretical results. A comparison with other methods demonstrates that the proposed method outperforms in adaptivity.

报告人简介：程昆，现为北京交通大学数学与统计学院讲师，研究方向为：统计学习理论、小波分析和函数数据分析及其应用。他的研究成果已发表在机器学习和概率统计领域的权威期刊。