题目：Hypotheses testing of functional principal components
汇报人：杨立坚
会议时间：2022年12月15日（星期四）14:00--15:00
交流平台：腾讯会议 414-527-871
报告人简介：
杨立坚，清华大学统计学研究中心与工业工程系长聘教授、国家特聘专家。北京大学数学学士（1987）、美国北卡罗来纳大学教堂山分校统计学博士（1995）、德国洪堡大学博士后（1995-97）。曾任美国密西根州立大学统计与概率系助理教授（1997-2001）、终身副教授（2001-06）、终身正教授（2006-14）、研究生主任（2007-10），苏州大学特聘教授、高等统计与计量经济中心主任（2011-16）。获美国耶鲁大学出版社Tjalling C. Koopmans Econometric Theory Prize、美国统计协会会士（ASA Fellow）、国际数理统计学会会士（IMS Fellow）、国际工程技术协会杰出会士（IETI Distinguished Fellow）、国际统计学会当选会员（ISI Elected Member）。研究领域：函数型数据、非线性时间序列数据、抽样调查数据的统计推断，高维数据的半参数降维，同时置信带的理论与方法，统计学对经济学、食品科学、遗传学、神经科学、和管理科学的应用。在包括Annals of Statistics, Annals of Probability, Journal of the American Statistical Association, Journal of the Royal Statistical Society B, Journal of Econometrics, Journal of Business and Economic Statistics 的SCI期刊发表论文80余篇。
摘要：
We propose a test for the hypothesis that the standardized functional principal components (FPCs) of a functional data equal a given set of orthonormal basis (e.g., the Fourier basis). Based on B-spline estimators of individual trajectories, a chi-square type statistic is constructed and shown to be oracally efficient under the null hypothesis in the sense that its limiting distribution is the same as an infeasible statistic using all trajectories, known by “oracle”. The null limiting distribution is an infinite Gaussian quadratic form, and a consistent estimator of its quantile is obtained. A test statistic based on the chi-square type statistic and approximate quantile of the Gaussian quadratic form is shown to be both of the nominal asymptotic significance level and asymptotically correct. Simulation studies illustrate superior finite sample performance of the proposed testing procedure. For the EEG (ElectroEncephalogram) data, the proposed procedure has confirmed an interesting discovery that the centered EEG data is generated from a small set of standard Fourier basis.
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