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Activity Number:
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271
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Type:
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Contributed
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Date/Time:
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Tuesday, August 5, 2008 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #301894 |
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Title:
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Functional Singular Value Decomposition and Applications
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Author(s):
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Wenjing Yang*+ and Hans G. Müller
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Companies:
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University of California, Davis and University of California, Davis
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Address:
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One Shields Ave, Davis, CA, 95616,
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Keywords:
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Functional data analysis ; Functional correlation ; Sparse data ; Covariance estimation
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Abstract:
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Inspired by the canonical expansion of compact operators in functional analysis, we develop the concept of functional singular value decomposition (fSVD). It is shown that both functional singular values and singular component functions can be consistently estimated even when data are observed sparsely and with measurement error as is the case in many longitudinal studies. Applications of fSVD include functional partial least squares and functional correlation. Due to the need to invert compact operators, some correlation measures in FDA such as functional canonical correlation are plagued by numerical instability. We apply fSVD to derive a stable functional correlation measure which is shown to be stable, and demonstrate its performance in simulations and applications.
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