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Activity Number:
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521
- Statistical Methods for Functional Data
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Type:
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Contributed
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Date/Time:
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Thursday, August 11, 2022 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #322717
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Title:
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Hypotheses Testing of Functional Principal Components
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Author(s):
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Zening Song* and Lijian Yang and Yuanyuan Zhang
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Companies:
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Tsinghua University and Tsinghua University and Soochow University
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Keywords:
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B-spline;
Functional principle components;
Gaussian quadratic form;
Oracle efficiency;
ElectroEncephalogram
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Abstract:
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This paper proposes a procedure to test the hypothesis that the functional principle components (FPCs) of a functional data equal a given set of orthonormal basis such as the Fourier basis. Based on B-spline estimators of individual trajectories, a test statistic is constructed and shown to be oracally efficient in the sense that its limiting distribution is the same as an infeasible statistic if all unobserved trajectories were known by “oracle”. The limiting distribution is shown to be an infinite Gaussian quadratic form, and a finite sample estimator of its quantile is shown to be consistent. Simulation studies are conducted to illustrate the finite performance of the proposed testing methods. For an EEG (ElectroEncephalogram) data, the proposed procedure has confirmed an interesting discovery that the data is generated from simple Fourier basis.
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Authors who are presenting talks have a * after their name.
