学术报告: Adaptive estimation for functional data: Using a framelet block-thresholding method

审核发布:数学与信息学院 来源单位及审核人: 发布时间:2022-05-04浏览次数:10

报告人:陈迪荣 教授(北京航空航天大学)

报告时间:2022年5月5日(周四) 上午10:00-11:00

报告地点:腾讯会议,会议号254115816

主办单位:太阳集团在线娱乐品牌数学与信息学院

 

报告摘要:Nonparametric estimation of mean and covariance functions based on discretely observed data is important in functional data analysis. In this talk, we propose a framelet block-thresholding method for estimating mean and covariance functions from discretely sampled noisy observations. Estimated convergence rates are established for all types of sampling schemes. In particular, the results reveal a phase transition phenomenon related to the number of observations on each curve. The procedures are adaptive in automatically adjusting the smoothness properties of the underlying mean and covariance functions. In contrast, theoretical results for other smoothing methods hold in the setting where smoothness parameters are assumed to be known, since the regularization parameters of estimators that depend on smoothness properties need to be chosen carefully. 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:陈迪荣,北京航空航天大学教授,北航“蓝天学者”特聘教授,博士生导师。1982年1月获学士学位,1992年7月获博士学位。主要从事统计学习理论,函数型数据分析,以及在国防工程技术中应用研究,取得了具有国际先进水平的成果,获教育部2012年度自然科学二等奖。先后主持国家自然科学基金8项,“863”课题3项,“973”计划子课题1项。发表SCI论文数十篇,其中多篇发表在权威刊物Appl. Computational Harmonic Analysis, Found. Computational Math., SIAM Math. Anal., SIAM Numerical Analysis, IEEE Transaction on Automatic Control, IEEE Trans Information Theory, Journal Machine Learning Research等上,单篇论文被SCI引用最高近两百次。

 

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